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<HTML>
<HEAD><title>On-Line SLICOT Overview</title></HEAD>
<BODY>
<H1>SLICOT LIBRARY INDEX</H1>
<HR>
To go to the beginning of a chapter click on the appropriate letter below: <p>
<center>
<A HREF = "#A"><B>A</B></A> ;
<A HREF = "#B"><B>B</B></A> ;
<A HREF = "#C"><B>C</B></A> ;
<A HREF = "#D"><B>D</B></A> ;
<A HREF = "#F"><B>F</B></A> ;
<A HREF = "#I"><B>I</B></A> ;
<A HREF = "#M"><B>M</B></A> ;
<A HREF = "#N"><B>N</B></A> ;
<A HREF = "#S"><B>S</B></A> ;
<A HREF = "#T"><B>T</B></A> ;
<A HREF = "#U"><B>U</B></A> ;
</center>
<BR>
or <A href="http://www.slicot.org/index.php?site=home">
<b>Return to SLICOT homepage</b></A>
<BR>
or <A href=".\doc\support.html">
<b>Go to SLICOT Supporting Routines Index</b></A>
<p>
<HR>
<A NAME="A"><H2>A - Analysis Routines</H2></A>
<h3>AB - State-Space Analysis</h3>
<h4>Canonical and Quasi Canonical Forms</h4>
<PRE>
<A href=".\doc\AB01MD.html">
<B>AB01MD</B></A> Orthogonal controllability form for single-input system
<A href=".\doc\AB01ND.html">
<B>AB01ND</B></A> Orthogonal controllability staircase form for multi-input system
<A href=".\doc\AB01OD.html">
<B>AB01OD</B></A> Staircase form for multi-input system using orthogonal transformations
</PRE>
<h4>Continuous/Discrete Time</h4>
<PRE>
<A href=".\doc\AB04MD.html">
<B>AB04MD</B></A> Discrete-time <-> continuous-time conversion by bilinear transformation
</PRE>
<h4>Interconnections of Subsystems</h4>
<PRE>
<A href=".\doc\AB05MD.html">
<B>AB05MD</B></A> Cascade inter-connection of two systems in state-space form
<A href=".\doc\AB05ND.html">
<B>AB05ND</B></A> Feedback inter-connection of two systems in state-space form
<A href=".\doc\AB05OD.html">
<B>AB05OD</B></A> Rowwise concatenation of two systems in state-space form
<A href=".\doc\AB05PD.html">
<B>AB05PD</B></A> Parallel inter-connection of two systems in state-space form
<A href=".\doc\AB05QD.html">
<B>AB05QD</B></A> Appending two systems in state-space form
<A href=".\doc\AB05RD.html">
<B>AB05RD</B></A> Closed-loop system for a mixed output and state feedback control law
<A href=".\doc\AB05SD.html">
<B>AB05SD</B></A> Closed-loop system for an output feedback control law
</PRE>
<h4>Inverse and Dual Systems</h4>
<PRE>
<A href=".\doc\AB07MD.html">
<B>AB07MD</B></A> Dual of a given state-space representation
<A href=".\doc\AB07ND.html">
<B>AB07ND</B></A> Inverse of a given state-space representation
</PRE>
<h4>Poles, Zeros, Gain</h4>
<PRE>
<A href=".\doc\AB08MD.html">
<B>AB08MD</B></A> Normal rank of the transfer-function matrix of a state space model
<A href=".\doc\AB08MZ.html">
<B>AB08MZ</B></A> Normal rank of the transfer-function matrix of a state space model (complex case)
<A href=".\doc\AB08ND.html">
<B>AB08ND</B></A> System zeros and Kronecker structure of system pencil
<A href=".\doc\AB08NW.html">
<B>AB08NW</B></A> System zeros and singular and infinite Kronecker structure of system pencil
<A href=".\doc\AB08NZ.html">
<B>AB08NZ</B></A> System zeros and Kronecker structure of system pencil (complex case)
</PRE>
<h4>Model Reduction</h4>
<PRE>
<A href=".\doc\AB09AD.html">
<B>AB09AD</B></A> Balance & Truncate model reduction
<A href=".\doc\AB09BD.html">
<B>AB09BD</B></A> Singular perturbation approximation based model reduction
<A href=".\doc\AB09CD.html">
<B>AB09CD</B></A> Hankel norm approximation based model reduction
<A href=".\doc\AB09DD.html">
<B>AB09DD</B></A> Singular perturbation approximation formulas
<A href=".\doc\AB09ED.html">
<B>AB09ED</B></A> Hankel norm approximation based model reduction of unstable systems
<A href=".\doc\AB09FD.html">
<B>AB09FD</B></A> Balance & Truncate model reduction of coprime factors
<A href=".\doc\AB09GD.html">
<B>AB09GD</B></A> Singular perturbation approximation of coprime factors
<A href=".\doc\AB09HD.html">
<B>AB09HD</B></A> Stochastic balancing based model reduction
<A href=".\doc\AB09ID.html">
<B>AB09ID</B></A> Frequency-weighted model reduction based on balancing techniques
<A href=".\doc\AB09JD.html">
<B>AB09JD</B></A> Frequency-weighted Hankel norm approximation with invertible weights
<A href=".\doc\AB09KD.html">
<B>AB09KD</B></A> Frequency-weighted Hankel-norm approximation
<A href=".\doc\AB09MD.html">
<B>AB09MD</B></A> Balance & Truncate model reduction for the stable part
<A href=".\doc\AB09ND.html">
<B>AB09ND</B></A> Singular perturbation approximation based model reduction for the
stable part
</PRE>
<h4>System Norms</h4>
<PRE>
<A href=".\doc\AB13AD.html">
<B>AB13AD</B></A> Hankel-norm of the stable projection
<A href=".\doc\AB13BD.html">
<B>AB13BD</B></A> H2 or L2 norm of a system
<A href=".\doc\AB13CD.html">
<B>AB13CD</B></A> H-infinity norm of a continuous-time stable system
(obsolete, replaced by AB13DD)
<A href=".\doc\AB13DD.html">
<B>AB13DD</B></A> L-infinity norm of a state space system
<A href=".\doc\AB13HD.html">
<B>AB13HD</B></A> L-infinity norm of a state space system in standard or
in descriptor form
<A href=".\doc\AB13ED.html">
<B>AB13ED</B></A> Complex stability radius, using bisection
<A href=".\doc\AB13FD.html">
<B>AB13FD</B></A> Complex stability radius, using bisection and SVD
<A href=".\doc\AB13ID.html">
<B>AB13ID</B></A> Properness of the transfer function matrix of a descriptor system
<A href=".\doc\AB13MD.html">
<B>AB13MD</B></A> Upper bound on the structured singular value for a square
complex matrix
</PRE>
<h3>AG - Generalized State-Space Analysis</h3>
<h4>Inverse and Dual Systems</h4>
<PRE>
<A href=".\doc\AG07BD.html">
<B>AG07BD</B></A> Descriptor inverse of a state-space or descriptor representation
</PRE>
<h4>Poles, Zeros, Gain</h4>
<PRE>
<A href=".\doc\AG08BD.html">
<B>AG08BD</B></A> Zeros and Kronecker structure of a descriptor system pencil
<A href=".\doc\AG08BZ.html">
<B>AG08BZ</B></A> Zeros and Kronecker structure of a descriptor system pencil (complex case)
</PRE>
<HR>
<A NAME="B"><H2>B - Benchmark and Test Problems</H2></A>
<h3>BB - State-space Models</h3>
<PRE>
<A href=".\doc\BB01AD.html">
<B>BB01AD</B></A> Benchmark examples for continuous-time Riccati equations
<A href=".\doc\BB02AD.html">
<B>BB02AD</B></A> Benchmark examples for discrete-time Riccati equations
<A href=".\doc\BB03AD.html">
<B>BB03AD</B></A> Benchmark examples of (generalized) continuous-time Lyapunov equations
<A href=".\doc\BB04AD.html">
<B>BB04AD</B></A> Benchmark examples of (generalized) discrete-time Lyapunov equations
</PRE>
<h3>BD - Generalized State-space Models</h3>
<PRE>
<A href=".\doc\BD01AD.html">
<B>BD01AD</B></A> Benchmark examples of continuous-time systems
<A href=".\doc\BD02AD.html">
<B>BD02AD</B></A> Benchmark examples of discrete-time systems
</PRE>
<HR>
<A NAME="C"><H2>C - Adaptive Control</H2></A>
<HR>
<A NAME="D"><H2>D - Data Analysis</H2></A>
<h3>DE - Covariances</h3>
<PRE>
<A href=".\doc\DE01OD.html">
<B>DE01OD</B></A> Convolution or deconvolution of two signals
<A href=".\doc\DE01PD.html">
<B>DE01PD</B></A> Convolution or deconvolution of two real signals using Hartley transform
</PRE>
<h3>DF - Spectra</h3>
<PRE>
<A href=".\doc\DF01MD.html">
<B>DF01MD</B></A> Sine transform or cosine transform of a real signal
</PRE>
<h3>DG - Discrete Fourier and Hartley Transforms</h3>
<PRE>
<A href=".\doc\DG01MD.html">
<B>DG01MD</B></A> Discrete Fourier transform of a complex signal
<A href=".\doc\DG01ND.html">
<B>DG01ND</B></A> Discrete Fourier transform of a real signal
<A href=".\doc\DG01OD.html">
<B>DG01OD</B></A> Scrambled discrete Hartley transform of a real signal
</PRE>
<h3>DK - Windowing</h3>
<PRE>
<A href=".\doc\DK01MD.html">
<B>DK01MD</B></A> Anti-aliasing window applied to a real signal
</PRE>
<HR>
<A NAME="F"><H2>F - Filtering</H2></A>
<h3>FB - Kalman Filters</h3>
<PRE>
<A href=".\doc\FB01QD.html">
<B>FB01QD</B></A> Time-varying square root covariance filter (dense matrices)
<A href=".\doc\FB01RD.html">
<B>FB01RD</B></A> Time-invariant square root covariance filter (Hessenberg form)
<A href=".\doc\FB01SD.html">
<B>FB01SD</B></A> Time-varying square root information filter (dense matrices)
<A href=".\doc\FB01TD.html">
<B>FB01TD</B></A> Time-invariant square root information filter (Hessenberg form)
<A href=".\doc\FB01VD.html">
<B>FB01VD</B></A> One recursion of the conventional Kalman filter
</PRE>
<h3>FD - Fast Recursive Least Squares Filters</h3>
<PRE>
<A href=".\doc\FD01AD.html">
<B>FD01AD</B></A> Fast recursive least-squares filter
</PRE>
<HR>
<A NAME="I"><H2>I - Identification</H2></A>
<h3>IB - Subspace Identification</h3>
<h4>Time Invariant State-space Systems</h4>
<PRE>
<A href=".\doc\IB01AD.html">
<B>IB01AD</B></A> Input-output data preprocessing and finding the system order
<A href=".\doc\IB01BD.html">
<B>IB01BD</B></A> Estimating the system matrices, covariances, and Kalman gain
<A href=".\doc\IB01CD.html">
<B>IB01CD</B></A> Estimating the initial state and the system matrices B and D
</PRE>
<h4>Wiener Systems</h4>
<PRE>
<A href=".\doc\IB03AD.html">
<B>IB03AD</B></A> Estimating a Wiener system by a Levenberg-Marquardt algorithm
(Cholesky-based or conjugate gradients solver)
<A href=".\doc\IB03BD.html">
<B>IB03BD</B></A> Estimating a Wiener system by a MINPACK-like Levenberg-Marquardt
algorithm
</PRE>
<HR>
<A NAME="M"><H2>M - Mathematical Routines</H2></A>
<h3>MB - Linear Algebra</h3>
<h4>Basic Linear Algebra Manipulations</h4>
<PRE>
<A href=".\doc\MB01PD.html">
<B>MB01PD</B></A> Matrix scaling (higher level routine)
<A href=".\doc\MB01QD.html">
<B>MB01QD</B></A> Matrix scaling (lower level routine)
<A href=".\doc\MB01RB.html">
<B>MB01RB</B></A> Computation of a triangle of matrix expression alpha*R + beta*A*B
or alpha*R + beta*B*A ( BLAS 3 version)
<A href=".\doc\MB01RD.html">
<B>MB01RD</B></A> Computation of matrix expression alpha*R + beta*A*X*trans(A)
<A href=".\doc\MB01TD.html">
<B>MB01TD</B></A> Product of two upper quasi-triangular matrices
<A href=".\doc\MB01UD.html">
<B>MB01UD</B></A> Computation of matrix expressions alpha*H*A or alpha*A*H,
with H an upper Hessenberg matrix
<A href=".\doc\MB01UX.html">
<B>MB01UX</B></A> Computation of matrix expressions alpha*T*A or alpha*A*T, T quasi-triangular
<A href=".\doc\MB01UY.html">
<B>MB01UY</B></A> Computation of matrix expressions alpha*T*A or alpha*A*T, over T, T triangular
<A href=".\doc\MB01UZ.html">
<B>MB01UZ</B></A> Computation of matrix expressions alpha*T*A or alpha*A*T, over T, T triangular
(complex version)
<A href=".\doc\MB01WD.html">
<B>MB01WD</B></A> Residuals of Lyapunov or Stein equations for Cholesky factored
solutions
<A href=".\doc\MB01XD.html">
<B>MB01XD</B></A> Computation of the product U'*U or L*L', with U and L upper and
lower triangular matrices (block algorithm)
<A href=".\doc\MB01YD.html">
<B>MB01YD</B></A> Symmetric rank k operation C := alpha*A*A' + beta*C, C symmetric
<A href=".\doc\MB01ZD.html">
<B>MB01ZD</B></A> Computation of matrix expressions H := alpha*T*H, or H := alpha*H*T,
with H Hessenberg-like, T triangular
</PRE>
<h4>Linear Equations and Least Squares</h4>
<PRE>
<A href=".\doc\MB02CD.html">
<B>MB02CD</B></A> Cholesky factorization of a positive definite block Toeplitz matrix
<A href=".\doc\MB02DD.html">
<B>MB02DD</B></A> Updating Cholesky factorization of a positive definite block
Toeplitz matrix
<A href=".\doc\MB02ED.html">
<B>MB02ED</B></A> Solution of T*X = B or X*T = B, with T a positive definite
block Toeplitz matrix
<A href=".\doc\MB02FD.html">
<B>MB02FD</B></A> Incomplete Cholesky factor of a positive definite block Toeplitz matrix
<A href=".\doc\MB02GD.html">
<B>MB02GD</B></A> Cholesky factorization of a banded symmetric positive definite
block Toeplitz matrix
<A href=".\doc\MB02HD.html">
<B>MB02HD</B></A> Cholesky factorization of the matrix T'*T, with T a banded
block Toeplitz matrix of full rank
<A href=".\doc\MB02ID.html">
<B>MB02ID</B></A> Solution of over- or underdetermined linear systems with a full rank
block Toeplitz matrix
<A href=".\doc\MB02JD.html">
<B>MB02JD</B></A> Full QR factorization of a block Toeplitz matrix of full rank
<A href=".\doc\MB02JX.html">
<B>MB02JX</B></A> Low rank QR factorization with column pivoting of a block Toeplitz matrix
<A href=".\doc\MB02KD.html">
<B>MB02KD</B></A> Computation of the product C = alpha*op( T )*B + beta*C, with T
a block Toeplitz matrix
<A href=".\doc\MB02MD.html">
<B>MB02MD</B></A> Solution of Total Least-Squares problem using a SVD approach
<A href=".\doc\MB02ND.html">
<B>MB02ND</B></A> Solution of Total Least-Squares problem using a partial SVD approach
<A href=".\doc\MB02OD.html">
<B>MB02OD</B></A> Solution of op(A)*X = alpha*B, or X*op(A) = alpha*B, A triangular
<A href=".\doc\MB02PD.html">
<B>MB02PD</B></A> Solution of matrix equation op(A)*X = B, with error bounds
and condition estimates
<A href=".\doc\MB02QD.html">
<B>MB02QD</B></A> Solution, optionally corresponding to specified free elements,
of a linear least squares problem
<A href=".\doc\MB02RD.html">
<B>MB02RD</B></A> Solution of a linear system with upper Hessenberg matrix
<A href=".\doc\MB02RZ.html">
<B>MB02RZ</B></A> Solution of a linear system with complex upper Hessenberg matrix
<A href=".\doc\MB02SD.html">
<B>MB02SD</B></A> LU factorization of an upper Hessenberg matrix
<A href=".\doc\MB02SZ.html">
<B>MB02SZ</B></A> LU factorization of a complex upper Hessenberg matrix
<A href=".\doc\MB02TD.html">
<B>MB02TD</B></A> Condition number of an upper Hessenberg matrix
<A href=".\doc\MB02TZ.html">
<B>MB02TZ</B></A> Condition number of a complex upper Hessenberg matrix
<A href=".\doc\MB02UD.html">
<B>MB02UD</B></A> Minimum norm least squares solution of op(R)*X = B, or X*op(R) = B,
using singular value decomposition (R upper triangular)
<A href=".\doc\MB02VD.html">
<B>MB02VD</B></A> Solution of X*op(A) = B
</PRE>
<h4>Eigenvalues and Eigenvectors</h4>
<PRE>
<A href=".\doc\MB03LF.html">
<B>MB03LF</B></A> Eigenvalues and right deflating subspace of a real
skew-Hamiltonian/Hamiltonian pencil in factored form
<A href=".\doc\MB03FZ.html">
<B>MB03FZ</B></A> Eigenvalues and right deflating subspace of a complex
skew-Hamiltonian/Hamiltonian pencil in factored form
<A href=".\doc\MB03LD.html">
<B>MB03LD</B></A> Eigenvalues and right deflating subspace of a real
skew-Hamiltonian/Hamiltonian pencil
<A href=".\doc\MB03LP.html">
<B>MB03LP</B></A> Eigenvalues and right deflating subspace of a real
skew-Hamiltonian/Hamiltonian pencil (applying transformations on panels of columns)
<A href=".\doc\MB03LZ.html">
<B>MB03LZ</B></A> Eigenvalues and right deflating subspace of a complex
skew-Hamiltonian/Hamiltonian pencil
<A href=".\doc\MB3LZP.html">
<B>MB3LZP</B></A> Eigenvalues and right deflating subspace of a complex
skew-Hamiltonian/Hamiltonian pencil (applying transformations on panels of columns)
<A href=".\doc\MB03MD.html">
<B>MB03MD</B></A> Upper bound for L singular values of a bidiagonal matrix
<A href=".\doc\MB03ND.html">
<B>MB03ND</B></A> Number of singular values of a bidiagonal matrix less than a bound
<A href=".\doc\MB03OD.html">
<B>MB03OD</B></A> Matrix rank determination by incremental condition estimation
<A href=".\doc\MB03PD.html">
<B>MB03PD</B></A> Matrix rank determination (row pivoting)
<A href=".\doc\MB03QD.html">
<B>MB03QD</B></A> Reordering of the diagonal blocks of a real Schur matrix
<A href=".\doc\MB03QG.html">
<B>MB03QG</B></A> Reordering of the diagonal blocks of principal subpencil of
a real Schur-triangular matrix pencil
<A href=".\doc\MB03RD.html">
<B>MB03RD</B></A> Reduction of a real Schur matrix to a block-diagonal form
<A href=".\doc\MB03RZ.html">
<B>MB03RZ</B></A> Reduction of a complex Schur matrix to a block-diagonal form
<A href=".\doc\MB03SD.html">
<B>MB03SD</B></A> Eigenvalues of a square-reduced Hamiltonian matrix
<A href=".\doc\MB03TD.html">
<B>MB03TD</B></A> Reordering the diagonal blocks of a matrix in (skew-)Hamiltonian Schur form
<A href=".\doc\MB03UD.html">
<B>MB03UD</B></A> Singular value decomposition of an upper triangular matrix
<A href=".\doc\MB03VD.html">
<B>MB03VD</B></A> Periodic Hessenberg form of a product of matrices
<A href=".\doc\MB03VW.html">
<B>MB03VW</B></A> Periodic Hessenberg form of a formal product of matrices
<A href=".\doc\MB03WD.html">
<B>MB03WD</B></A> Periodic Schur decomposition and eigenvalues of a product of
matrices in periodic Hessenberg form
<A href=".\doc\MB03XD.html">
<B>MB03XD</B></A> Eigenvalues of a Hamiltonian matrix
<A href=".\doc\MB03XZ.html">
<B>MB03XZ</B></A> Eigenvalues of a complex Hamiltonian matrix
<A href=".\doc\MB03XP.html">
<B>MB03XP</B></A> Periodic Schur decomposition and eigenvalues of a matrix product A*B,
A upper Hessenberg and B upper triangular
<A href=".\doc\MB03YD.html">
<B>MB03YD</B></A> Periodic QR iteration
<A href=".\doc\MB03ZD.html">
<B>MB03ZD</B></A> Stable and unstable invariant subspaces for a dichotomic Hamiltonian matrix
</PRE>
<h4>Decompositions and Transformations</h4>
<PRE>
<A href=".\doc\MB04AD.html">
<B>MB04AD</B></A> Eigenvalues and generalized symplectic URV decomposition of a real
skew-Hamiltonian/Hamiltonian pencil in factored form
<A href=".\doc\MB04AZ.html">
<B>MB04AZ</B></A> Eigenvalues of a complex skew-Hamiltonian/Hamiltonian pencil in factored form
<A href=".\doc\MB04BD.html">
<B>MB04BD</B></A> Eigenvalues and orthogonal decomposition of a real
skew-Hamiltonian/Hamiltonian pencil
<A href=".\doc\MB04BP.html">
<B>MB04BP</B></A> Eigenvalues and orthogonal decomposition of a real
skew-Hamiltonian/Hamiltonian pencil (applying transformations on panels of columns)
<A href=".\doc\MB04BZ.html">
<B>MB04BZ</B></A> Eigenvalues of a complex skew-Hamiltonian/Hamiltonian pencil
<A href=".\doc\MB04DL.html">
<B>MB04DL</B></A> Balancing a real matrix pencil, optionally avoiding large
norms for the scaled (sub)matrices
<A href=".\doc\MB4DLZ.html">
<B>MB4DLZ</B></A> Balancing a complex matrix pencil, optionally avoiding large
norms for the scaled (sub)matrices
<A href=".\doc\MB04DP.html">
<B>MB04DP</B></A> Balancing a real skew-Hamiltonian/Hamiltonian matrix pencil,
optionally avoiding large norms for the scaled (sub)matrices
<A href=".\doc\MB4DPZ.html">
<B>MB4DPZ</B></A> Balancing a complex skew-Hamiltonian/Hamiltonian matrix pencil,
optionally avoiding large norms for the scaled (sub)matrices
<A href=".\doc\MB04ED.html">
<B>MB04ED</B></A> Eigenvalues and orthogonal decomposition of a real
skew-Hamiltonian/skew-Hamiltonian pencil in factored form
<A href=".\doc\MB04FD.html">
<B>MB04FD</B></A> Eigenvalues and orthogonal decomposition of a real
skew-Hamiltonian/skew-Hamiltonian pencil
<A href=".\doc\MB04FP.html">
<B>MB04FP</B></A> Eigenvalues and orthogonal decomposition of a real
skew-Hamiltonian/skew-Hamiltonian pencil (applying transformations on panels of columns)
<A href=".\doc\MB04GD.html">
<B>MB04GD</B></A> RQ factorization of a matrix with row pivoting
<A href=".\doc\MB04ID.html">
<B>MB04ID</B></A> QR factorization of a matrix with a lower left zero triangle
<A href=".\doc\MB04IZ.html">
<B>MB04IZ</B></A> QR factorization of a matrix with a lower left zero triangle (complex case)
<A href=".\doc\MB04JD.html">
<B>MB04JD</B></A> LQ factorization of a matrix with an upper right zero triangle
<A href=".\doc\MB04KD.html">
<B>MB04KD</B></A> QR factorization of a special structured block matrix
<A href=".\doc\MB04LD.html">
<B>MB04LD</B></A> LQ factorization of a special structured block matrix
<A href=".\doc\MB04MD.html">
<B>MB04MD</B></A> Balancing a general real matrix
<A href=".\doc\MB04ND.html">
<B>MB04ND</B></A> RQ factorization of a special structured block matrix
<A href=".\doc\MB04OD.html">
<B>MB04OD</B></A> QR factorization of a special structured block matrix (variant)
<A href=".\doc\MB04PB.html">
<B>MB04PB</B></A> Paige/Van Loan form of a Hamiltonian matrix
<A href=".\doc\MB04RD.html">
<B>MB04RD</B></A> Reduction of a real matrix pencil in generalized real Schur form to
a block-diagonal form
<A href=".\doc\MB04RT.html">
<B>MB04RT</B></A> Solution of a generalized real Sylvester equation with matrix pairs
in generalized real Schur form (blocked version)
<A href=".\doc\MB04RW.html">
<B>MB04RW</B></A> Solution of a generalized complex Sylvester equation with matrix pairs
in generalized complex Schur form (blocked version)
<A href=".\doc\MB04RZ.html">
<B>MB04RZ</B></A> Reduction of a complex matrix pencil in generalized complex Schur form to
a block-diagonal form
<A href=".\doc\MB04TB.html">
<B>MB04TB</B></A> Symplectic URV decomposition of a real 2N-by-2N matrix
<A href=".\doc\MB04UD.html">
<B>MB04UD</B></A> Unitary column echelon form for a rectangular matrix
<A href=".\doc\MB04VD.html">
<B>MB04VD</B></A> Upper block triangular form for a rectangular pencil
<A href=".\doc\MB04XD.html">
<B>MB04XD</B></A> Basis for left/right null singular subspace of a matrix
<A href=".\doc\MB04YD.html">
<B>MB04YD</B></A> Partial diagonalization of a bidiagonal matrix
<A href=".\doc\MB04ZD.html">
<B>MB04ZD</B></A> Transforming a Hamiltonian matrix into a square-reduced form
</PRE>
<h4>Matrix Functions</h4>
<PRE>
<A href=".\doc\MB05MD.html">
<B>MB05MD</B></A> Matrix exponential for a real non-defective matrix
<A href=".\doc\MB05ND.html">
<B>MB05ND</B></A> Matrix exponential and integral for a real matrix
<A href=".\doc\MB05OD.html">
<B>MB05OD</B></A> Matrix exponential for a real matrix, with accuracy estimate
</PRE>
<h3>MC - Polynomial and Rational Function Manipulation</h3>
<h4>Scalar Polynomials</h4>
<PRE>
<A href=".\doc\MC01MD.html">
<B>MC01MD</B></A> The leading coefficients of the shifted polynomial
<A href=".\doc\MC01ND.html">
<B>MC01ND</B></A> Value of a real polynomial at a given complex point
<A href=".\doc\MC01OD.html">
<B>MC01OD</B></A> Coefficients of a complex polynomial, given its zeros
<A href=".\doc\MC01PD.html">
<B>MC01PD</B></A> Coefficients of a real polynomial, given its zeros
<A href=".\doc\MC01QD.html">
<B>MC01QD</B></A> Quotient and remainder polynomials for polynomial division
<A href=".\doc\MC01RD.html">
<B>MC01RD</B></A> Polynomial operation P(x) = P1(x) P2(x) + alpha P3(x)
<A href=".\doc\MC01SD.html">
<B>MC01SD</B></A> Scaling coefficients of a real polynomial for minimal variation
<A href=".\doc\MC01TD.html">
<B>MC01TD</B></A> Checking stability of a given real polynomial
<A href=".\doc\MC01VD.html">
<B>MC01VD</B></A> Roots of a quadratic equation with real coefficients
<A href=".\doc\MC01WD.html">
<B>MC01WD</B></A> Quotient and remainder polynomials for a quadratic denominator
<A href=".\doc\MC01XD.html">
<B>MC01XD</B></A> Roots of a third order polynomial
</PRE>
<h4>Polynomial Matrices</h4>
<PRE>
<A href=".\doc\MC03MD.html">
<B>MC03MD</B></A> Real polynomial matrix operation P(x) = P1(x) P2(x) + alpha P3(x)
<A href=".\doc\MC03ND.html">
<B>MC03ND</B></A> Minimal polynomial basis for the right nullspace of a polynomial matrix
</PRE>
<h3>MD - Optimization</h3>
<h4>Unconstrained Nonlinear Least Squares</h4>
<PRE>
<A href=".\doc\MD03AD.html">
<B>MD03AD</B></A> Levenberg-Marquardt algorithm (Cholesky-based or conjugate
gradients solver)
<A href=".\doc\MD03BD.html">
<B>MD03BD</B></A> Enhanced MINPACK-like Levenberg-Marquardt algorithm
</PRE>
<HR>
<A NAME="N"><H2>N - Nonlinear Systems</H2></A>
<h3>NI - Interfaces to Nonlinear Solvers</h3>
<h4>ODE and DAE Solvers</h4>
<PRE>
<A href=".\doc\DAESolver.html">
<B>DAESolver</B></A> Interface to DAE Solvers
<A href=".\doc\ODESolver.html">
<B>ODESolver</B></A> Interface to ODE Solvers
</PRE>
<h4>Nonlinear Equation Solvers</h4>
<PRE>
<A href=".\doc\KINSOL.html">
<B>KINSOL</B></A> Interface to KINSOL solver for nonlinear systems of equations
</PRE>
<h4>Nonlinear Optimization Solvers</h4>
<PRE>
<A href=".\doc\FSQP.html">
<B>FSQP</B></A> Interface to FSQP solver for nonlinear optimization
</PRE>
<HR>
<A NAME="S"><H2>S - Synthesis Routines</H2></A>
<h3>SB - State-Space Synthesis</h3>
<h4>Eigenvalue/Eigenvector Assignment</h4>
<PRE>
<A href=".\doc\SB01BD.html">
<B>SB01BD</B></A> Pole assignment for a given matrix pair (A,B)
<A href=".\doc\SB01DD.html">
<B>SB01DD</B></A> Eigenstructure assignment for a controllable matrix pair (A,B) in
orthogonal canonical form
<A href=".\doc\SB01MD.html">
<B>SB01MD</B></A> State feedback matrix of a time-invariant single-input system
</PRE>
<h4>Riccati Equations</h4>
<PRE>
<A href=".\doc\SB02MD.html">
<B>SB02MD</B></A> Solution of algebraic Riccati equations (Schur vectors method)
<A href=".\doc\SB02MT.html">
<B>SB02MT</B></A> Conversion of problems with coupling terms to standard problems
<A href=".\doc\SB02MX.html">
<B>SB02MX</B></A> Conversion of problems with coupling terms to standard problems
(more flexibility)
<A href=".\doc\SB02ND.html">
<B>SB02ND</B></A> Optimal state feedback matrix for an optimal control problem
<A href=".\doc\SB02OD.html">
<B>SB02OD</B></A> Solution of algebraic Riccati equations (generalized Schur method)
<A href=".\doc\SB02PD.html">
<B>SB02PD</B></A> Solution of continuous algebraic Riccati equations (matrix sign
function method) with condition and forward error bound estimates
<A href=".\doc\SB02QD.html">
<B>SB02QD</B></A> Condition and forward error for continuous Riccati equation solution
<A href=".\doc\SB02RD.html">
<B>SB02RD</B></A> Solution of algebraic Riccati equations (refined Schur vectors method)
with condition and forward error bound estimates
<A href=".\doc\SB02SD.html">
<B>SB02SD</B></A> Condition and forward error for discrete Riccati equation solution
</PRE>
<h4>Lyapunov Equations</h4>
<PRE>
<A href=".\doc\SB03MD.html">
<B>SB03MD</B></A> Solution of Lyapunov equations and separation estimation
<A href=".\doc\SB03OD.html">
<B>SB03OD</B></A> Solution of stable Lyapunov equations (Cholesky factor)
<A href=".\doc\SB03OZ.html">
<B>SB03OZ</B></A> Solution of stable complex Lyapunov equations (Cholesky factor)
<A href=".\doc\SB03PD.html">
<B>SB03PD</B></A> Solution of discrete Lyapunov equations and separation estimation
<A href=".\doc\SB03QD.html">
<B>SB03QD</B></A> Condition and forward error for continuous Lyapunov equations
<A href=".\doc\SB03RD.html">
<B>SB03RD</B></A> Solution of continuous Lyapunov equations and separation estimation
<A href=".\doc\SB03SD.html">
<B>SB03SD</B></A> Condition and forward error for discrete Lyapunov equations
<A href=".\doc\SB03TD.html">
<B>SB03TD</B></A> Solution of continuous Lyapunov equations, condition and forward error
estimation
<A href=".\doc\SB03UD.html">
<B>SB03UD</B></A> Solution of discrete Lyapunov equations, condition and forward error
estimation
</PRE>
<h4>Sylvester Equations</h4>
<PRE>
<A href=".\doc\SB04MD.html">
<B>SB04MD</B></A> Solution of continuous Sylvester equations (Hessenberg-Schur method)
<A href=".\doc\SB04ND.html">
<B>SB04ND</B></A> Solution of continuous Sylvester equations (one matrix in Schur form)
<A href=".\doc\SB04OD.html">
<B>SB04OD</B></A> Solution of generalized Sylvester equations with separation estimation
<A href=".\doc\SB04PD.html">
<B>SB04PD</B></A> Solution of continuous or discrete Sylvester equations (Schur method)
<A href=".\doc\SB04QD.html">
<B>SB04QD</B></A> Solution of discrete Sylvester equations (Hessenberg-Schur method)
<A href=".\doc\SB04RD.html">
<B>SB04RD</B></A> Solution of discrete Sylvester equations (one matrix in Schur form)
</PRE>
<h4>Deadbeat Control</h4>
<PRE>
<A href=".\doc\SB06ND.html">
<B>SB06ND</B></A> Minimum norm deadbeat control state feedback matrix
</PRE>
<h4>Transfer Matrix Factorization</h4>
<PRE>
<A href=".\doc\SB08CD.html">
<B>SB08CD</B></A> Left coprime factorization with inner denominator
<A href=".\doc\SB08DD.html">
<B>SB08DD</B></A> Right coprime factorization with inner denominator
<A href=".\doc\SB08ED.html">
<B>SB08ED</B></A> Left coprime factorization with prescribed stability degree
<A href=".\doc\SB08FD.html">
<B>SB08FD</B></A> Right coprime factorization with prescribed stability degree
<A href=".\doc\SB08GD.html">
<B>SB08GD</B></A> State-space representation of a left coprime factorization
<A href=".\doc\SB08HD.html">
<B>SB08HD</B></A> State-space representation of a right coprime factorization
<A href=".\doc\SB08MD.html">
<B>SB08MD</B></A> Spectral factorization of polynomials (continuous-time case)
<A href=".\doc\SB08ND.html">
<B>SB08ND</B></A> Spectral factorization of polynomials (discrete-time case)
</PRE>
<h4>Realization Methods</h4>
<PRE>
<A href=".\doc\SB09MD.html">
<B>SB09MD</B></A> Closeness of two multivariable sequences
</PRE>
<h4>Optimal Regulator Problems</h4>
<PRE>
<A href=".\doc\SB10AD.html">
<B>SB10AD</B></A> H-infinity optimal controller using modified Glover's and Doyle's
formulas (continuous-time)
<A href=".\doc\SB10DD.html">
<B>SB10DD</B></A> H-infinity (sub)optimal state controller for a discrete-time system
<A href=".\doc\SB10ED.html">
<B>SB10ED</B></A> H2 optimal state controller for a discrete-time system
<A href=".\doc\SB10FD.html">
<B>SB10FD</B></A> H-infinity (sub)optimal state controller for a continuous-time system
<A href=".\doc\SB10HD.html">
<B>SB10HD</B></A> H2 optimal state controller for a continuous-time system
<A href=".\doc\SB10MD.html">
<B>SB10MD</B></A> D-step in the D-K iteration for continuous-time case
<A href=".\doc\SB10ID.html">
<B>SB10ID</B></A> Positive feedback controller for a continuous-time system
<A href=".\doc\SB10KD.html">
<B>SB10KD</B></A> Positive feedback controller for a discrete-time system
<A href=".\doc\SB10ZD.html">
<B>SB10ZD</B></A> Positive feedback controller for a discrete-time system (D <> 0)
</PRE>
<h4>Controller Reduction</h4>
<PRE>
<A href=".\doc\SB16AD.html">
<B>SB16AD</B></A> Stability/performance enforcing frequency-weighted controller reduction
<A href=".\doc\SB16BD.html">
<B>SB16BD</B></A> Coprime factorization based state feedback controller reduction
<A href=".\doc\SB16CD.html">
<B>SB16CD</B></A> Coprime factorization based frequency-weighted state feedback
controller reduction
</PRE>
<h3>SG - Generalized State-Space Synthesis</h3>
<h4>Riccati Equations</h4>
<PRE>
<A href=".\doc\SG02AD.html">
<B>SG02AD</B></A> Solution of algebraic Riccati equations for descriptor systems
<A href=".\doc\SG02CW.html">
<B>SG02CW</B></A> Residual of continuous- or discrete-time (generalized) algebraic
Riccati equations
<A href=".\doc\SG02CX.html">
<B>SG02CX</B></A> Line search parameter minimizing the residual of (generalized)
continuous- or discrete-time algebraic Riccati equations
<A href=".\doc\SG02ND.html">
<B>SG02ND</B></A> Optimal state feedback matrix for an optimal control problem
</PRE>
<h4>Generalized Lyapunov Equations</h4>
<PRE>
<A href=".\doc\SG03AD.html">
<B>SG03AD</B></A> Solution of generalized Lyapunov equations and separation estimation
<A href=".\doc\SG03BD.html">
<B>SG03BD</B></A> Solution of stable generalized Lyapunov equations (Cholesky factor)
<A href=".\doc\SG03BZ.html">
<B>SG03BZ</B></A> Solution of stable generalized complex Lyapunov equations (Cholesky factor)
</PRE>
<HR>
<A NAME="T"><H2>T - Transformation Routines</H2></A>
<h3>TB - State-Space</h3>
<h4>State-Space Transformations</h4>
<PRE>
<A href=".\doc\TB01ID.html">
<B>TB01ID</B></A> Balancing a system matrix for a given triplet
<A href=".\doc\TB01IZ.html">
<B>TB01IZ</B></A> Balancing a system matrix for a given triplet (complex case)
<A href=".\doc\TB01KD.html">
<B>TB01KD</B></A> Additive spectral decomposition of a state-space system
<A href=".\doc\TB01LD.html">
<B>TB01LD</B></A> Spectral separation of a state-space system
<A href=".\doc\TB01MD.html">
<B>TB01MD</B></A> Upper/lower controller Hessenberg form
<A href=".\doc\TB01ND.html">
<B>TB01ND</B></A> Upper/lower observer Hessenberg form
<A href=".\doc\TB01PD.html">
<B>TB01PD</B></A> Minimal, controllable or observable block Hessenberg realization
<A href=".\doc\TB01PX.html">
<B>TB01PX</B></A> Minimal, controllable or observable block Hessenberg realization (variant)
<A href=".\doc\TB01TD.html">
<B>TB01TD</B></A> Balancing state-space representation by permutations and scalings
<A href=".\doc\TB01UD.html">
<B>TB01UD</B></A> Controllable block Hessenberg realization for a state-space representation
<A href=".\doc\TB01UY.html">
<B>TB01UY</B></A> Controllable block Hessenberg realization for a standard multi-input system
<A href=".\doc\TB01WD.html">
<B>TB01WD</B></A> Reduction of the state dynamics matrix to real Schur form
<A href=".\doc\TB01WX.html">
<B>TB01WX</B></A> Orthogonal similarity transformation of a standard system to one
with state matrix in a Hessenberg form
<A href=".\doc\TB01ZD.html">
<B>TB01ZD</B></A> Controllable realization for single-input systems
</PRE>
<h4>State-Space to Polynomial Matrix Conversion</h4>
<PRE>
<A href=".\doc\TB03AD.html">
<B>TB03AD</B></A> Left/right polynomial matrix representation of a state-space representation
</PRE>
<h4>State-Space to Rational Matrix Conversion</h4>
<PRE>
<A href=".\doc\TB04AD.html">
<B>TB04AD</B></A> Transfer matrix of a state-space representation
<A href=".\doc\TB04BD.html">
<B>TB04BD</B></A> Transfer matrix of a state-space representation, using the pole-zeros method
<A href=".\doc\TB04CD.html">
<B>TB04CD</B></A> Transfer matrix of a state-space representation in the pole-zero-gain form
</PRE>
<h4>State-Space to Frequency Response</h4>
<PRE>
<A href=".\doc\TB05AD.html">
<B>TB05AD</B></A> Frequency response matrix of a state-space representation
</PRE>
<h3>TC - Polynomial Matrix</h3>
<h4>Polynomial Matrix Transformations</h4>
<PRE>
<A href=".\doc\TC01OD.html">
<B>TC01OD</B></A> Dual of a left/right polynomial matrix representation
</PRE>
<h4>Polynomial Matrix to State-Space Conversion</h4>
<PRE>
<A href=".\doc\TC04AD.html">
<B>TC04AD</B></A> State-space representation for left/right polynomial matrix representation
</PRE>
<h4>Polynomial Matrix to Frequency Response</h4>
<PRE>
<A href=".\doc\TC05AD.html">
<B>TC05AD</B></A> Transfer matrix of a left/right polynomial matrix representation
</PRE>
<h3>TD - Rational Matrix</h3>
<h4>Rational Matrix to Polynomial Matrix Conversion</h4>
<PRE>
<A href=".\doc\TD03AD.html">
<B>TD03AD</B></A> Left/right polynomial matrix representation for a proper transfer matrix
</PRE>
<h4>Rational Matrix to State-Space Conversion</h4>
<PRE>
<A href=".\doc\TD04AD.html">
<B>TD04AD</B></A> Minimal state-space representation for a proper transfer matrix
</PRE>
<h4>Rational Matrix to Frequency Response</h4>
<PRE>
<A href=".\doc\TD05AD.html">
<B>TD05AD</B></A> Evaluation of a transfer function for a specified frequency
</PRE>
<h3>TF - Time Response</h3>
<PRE>
<A href=".\doc\TF01MD.html">
<B>TF01MD</B></A> Output response of a linear discrete-time system
<A href=".\doc\TF01ND.html">
<B>TF01ND</B></A> Output response of a linear discrete-time system (Hessenberg matrix)
<A href=".\doc\TF01OD.html">
<B>TF01OD</B></A> Block Hankel expansion of a multivariable parameter sequence
<A href=".\doc\TF01PD.html">
<B>TF01PD</B></A> Block Toeplitz expansion of a multivariable parameter sequence
<A href=".\doc\TF01QD.html">
<B>TF01QD</B></A> Markov parameters of a system from transfer function matrix
<A href=".\doc\TF01RD.html">
<B>TF01RD</B></A> Markov parameters of a system from state-space representation
</PRE>
<h3>TG - Generalized State-space</h3>
<h4>Generalized State-space Transformations</h4>
<PRE>
<A href=".\doc\TG01AD.html">
<B>TG01AD</B></A> Balancing the matrices of the system pencil corresponding to a
descriptor triple
<A href=".\doc\TG01AZ.html">
<B>TG01AZ</B></A> Balancing the matrices of the system pencil corresponding to a
descriptor triple (complex case)
<A href=".\doc\TG01BD.html">
<B>TG01BD</B></A> Orthogonal reduction of a descriptor system to the generalized
Hessenberg form
<A href=".\doc\TG01CD.html">
<B>TG01CD</B></A> Orthogonal reduction of a descriptor system pair (A-sE,B)
to the QR-coordinate form
<A href=".\doc\TG01DD.html">
<B>TG01DD</B></A> Orthogonal reduction of a descriptor system pair (C,A-sE)
to the RQ-coordinate form
<A href=".\doc\TG01ED.html">
<B>TG01ED</B></A> Orthogonal reduction of a descriptor system to a SVD coordinate
form
<A href=".\doc\TG01FD.html">
<B>TG01FD</B></A> Orthogonal reduction of a descriptor system to a SVD-like
coordinate form
<A href=".\doc\TG01FZ.html">
<B>TG01FZ</B></A> Orthogonal reduction of a descriptor system to a SVD-like
coordinate form (complex case)
<A href=".\doc\TG01GD.html">
<B>TG01GD</B></A> Reduced descriptor representation without non-dynamic modes
<A href=".\doc\TG01HD.html">
<B>TG01HD</B></A> Orthogonal reduction of a descriptor system to the controllability
staircase form
<A href=".\doc\TG01ID.html">
<B>TG01ID</B></A> Orthogonal reduction of a descriptor system to the observability
staircase form
<A href=".\doc\TG01JD.html">
<B>TG01JD</B></A> Irreducible descriptor representation
<A href=".\doc\TG01JY.html">
<B>TG01JY</B></A> Irreducible descriptor representation (blocked version)
<A href=".\doc\TG01LD.html">
<B>TG01LD</B></A> Finite-infinite decomposition of a descriptor system
<A href=".\doc\TG01MD.html">
<B>TG01MD</B></A> Finite-infinite generalized real Schur form decomposition of a descriptor system
<A href=".\doc\TG01ND.html">
<B>TG01ND</B></A> Finite-infinite block-diagonal decomposition of a descriptor system
<A href=".\doc\TG01OD.html">
<B>TG01OD</B></A> Reducing a SISO descriptor system with E nonsingular so that
the obtained feedthrough term has a sufficiently large magnitude
<A href=".\doc\TG01OZ.html">
<B>TG01OZ</B></A> Reducing a complex SISO descriptor system with E nonsingular so that
the obtained feedthrough term has a sufficiently large magnitude
<A href=".\doc\TG01PD.html">
<B>TG01PD</B></A> Bi-domain spectral splitting of a subpencil of a descriptor system
<A href=".\doc\TG01QD.html">
<B>TG01QD</B></A> Three-domain spectral splitting of a subpencil of a descriptor system
<A href=".\doc\TG01WD.html">
<B>TG01WD</B></A> Reduction of the descriptor dynamics matrix pair to generalized
real Schur form
</PRE>
<HR>
<A NAME="U"><H2>U - Utility Routines</H2></A>
<h3>UD - Numerical Data Handling</h3>
<PRE>
<A href=".\doc\UD01BD.html">
<B>UD01BD</B></A> Reading a matrix polynomial
<A href=".\doc\UD01CD.html">
<B>UD01CD</B></A> Reading a sparse matrix polynomial
<A href=".\doc\UD01DD.html">
<B>UD01DD</B></A> Reading a sparse real matrix
<A href=".\doc\UD01MD.html">
<B>UD01MD</B></A> Printing a real matrix
<A href=".\doc\UD01MZ.html">
<B>UD01MZ</B></A> Printing a real matrix (complex case)
<A href=".\doc\UD01ND.html">
<B>UD01ND</B></A> Printing a matrix polynomial
<A href=".\doc\UE01MD.html">
<B>UE01MD</B></A> Default machine-specific parameters for (skew-)Hamiltonian computation routines
</PRE>
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