Spelling suggestions: "subject:"matrix sig function""
1 |
DGRSVX and DMSRIC: Fortran 77 subroutines for solving continuous-time matrix algebraic Riccati equations with condition and accuracy estimatesPetkov, P. Hr., Konstantinov, M. M., Mehrmann, V. 12 September 2005 (has links) (PDF)
We present new Fortran 77 subroutines which implement the Schur method and the
matrix sign function method for the solution of the continuoustime matrix algebraic
Riccati equation on the basis of LAPACK subroutines. In order to avoid some of
the wellknown difficulties with these methods due to a loss of accuracy, we combine
the implementations with block scalings as well as condition estimates and forward
error estimates. Results of numerical experiments comparing the performance of both
methods for more than one hundred well and illconditioned Riccati equations of order
up to 150 are given. It is demonstrated that there exist several classes of examples for
which the matrix sign function approach performs more reliably and more accurately
than the Schur method. In all cases the forward error estimates allow to obtain a reliable
bound on the accuracy of the computed solution.
|
2 |
Solving stable generalized Lyapunov equations with the matrix sign functionBenner, Peter, Quintana-Ortí, Enrique S. 07 September 2005 (has links) (PDF)
We investigate the numerical solution of the stable generalized Lyapunov equation via the sign function method. This approach has already been proposed to solve standard Lyapunov equations in several publications. The extension to the generalized case is straightforward. We consider some modifications and discuss how to solve generalized Lyapunov equations with semidefinite constant term for the Cholesky factor. The basic computational tools of the method are basic linear algebra operations that can be implemented efficiently on modern computer architectures and in particular on parallel computers. Hence, a considerable speed-up as compared to the Bartels-Stewart and Hammarling's methods is to be expected. We compare the algorithms by performing a variety of numerical tests.
|
3 |
Solving Linear Matrix Equations via Rational Iterative SchemesBenner, Peter, Quintana-Ortí, Enrique, Quintana-Ortí, Gregorio 01 September 2006 (has links) (PDF)
We investigate the numerical solution of stable Sylvester equations via iterative schemes proposed for computing the sign function of a matrix. In particular, we discuss how the rational iterations for the matrix sign function can efficiently be adapted to the special structure implied by the Sylvester equation. For Sylvester equations with factored constant term as those arising in model reduction or image restoration, we derive an algorithm that computes the solution in factored form directly. We also suggest convergence criteria for the resulting iterations and compare the accuracy and performance of the resulting methods with existing Sylvester solvers. The algorithms proposed here are easy to parallelize. We report on the parallelization of those algorithms and demonstrate their high efficiency and scalability using experimental results obtained on a cluster of Intel Pentium Xeon processors.
|
4 |
Solving Large-Scale Generalized Algebraic Bernoulli Equations via the Matrix Sign FunctionBarrachina, Sergio, Benner, Peter, Quintana-Ortí, Enrique S. 11 September 2006 (has links) (PDF)
We investigate the solution of large-scale generalized algebraic Bernoulli equations as those arising in control and systems theory in the context of stabilization of linear dynamical systems, coprime factorization of rational matrix-valued functions, and model reduction. The algorithms we propose, based on a generalization of the Newton iteration for the matrix sign function, are easy to parallelize, yielding an efficient numerical tool to solve large-scale problems. Both the accuracy and the parallel performance of our implementations on a cluster of Intel Xeon processors are reported.
|
5 |
The Matrix Sign Function Method and the Computation of Invariant SubspacesByers, R., He, C., Mehrmann, V. 30 October 1998 (has links) (PDF)
A perturbation analysis shows that if a numerically stable
procedure is used to compute the matrix sign function, then it is competitive
with conventional methods for computing invariant subspaces.
Stability analysis of the Newton iteration improves an earlier result of Byers
and confirms that ill-conditioned iterates may cause numerical
instability. Numerical examples demonstrate the theoretical results.
|
6 |
Solving Large-Scale Generalized Algebraic Bernoulli Equations via the Matrix Sign FunctionBarrachina, Sergio, Benner, Peter, Quintana-Ortí, Enrique S. 11 September 2006 (has links)
We investigate the solution of large-scale generalized algebraic Bernoulli equations as those arising in control and systems theory in the context of stabilization of linear dynamical systems, coprime factorization of rational matrix-valued functions, and model reduction. The algorithms we propose, based on a generalization of the Newton iteration for the matrix sign function, are easy to parallelize, yielding an efficient numerical tool to solve large-scale problems. Both the accuracy and the parallel performance of our implementations on a cluster of Intel Xeon processors are reported.
|
7 |
Solving stable generalized Lyapunov equations with the matrix sign functionBenner, Peter, Quintana-Ortí, Enrique S. 07 September 2005 (has links)
We investigate the numerical solution of the stable generalized Lyapunov equation via the sign function method. This approach has already been proposed to solve standard Lyapunov equations in several publications. The extension to the generalized case is straightforward. We consider some modifications and discuss how to solve generalized Lyapunov equations with semidefinite constant term for the Cholesky factor. The basic computational tools of the method are basic linear algebra operations that can be implemented efficiently on modern computer architectures and in particular on parallel computers. Hence, a considerable speed-up as compared to the Bartels-Stewart and Hammarling's methods is to be expected. We compare the algorithms by performing a variety of numerical tests.
|
8 |
DGRSVX and DMSRIC: Fortran 77 subroutines for solving continuous-time matrix algebraic Riccati equations with condition and accuracy estimatesPetkov, P. Hr., Konstantinov, M. M., Mehrmann, V. 12 September 2005 (has links)
We present new Fortran 77 subroutines which implement the Schur method and the
matrix sign function method for the solution of the continuoustime matrix algebraic
Riccati equation on the basis of LAPACK subroutines. In order to avoid some of
the wellknown difficulties with these methods due to a loss of accuracy, we combine
the implementations with block scalings as well as condition estimates and forward
error estimates. Results of numerical experiments comparing the performance of both
methods for more than one hundred well and illconditioned Riccati equations of order
up to 150 are given. It is demonstrated that there exist several classes of examples for
which the matrix sign function approach performs more reliably and more accurately
than the Schur method. In all cases the forward error estimates allow to obtain a reliable
bound on the accuracy of the computed solution.
|
9 |
The Matrix Sign Function Method and the Computation of Invariant SubspacesByers, R., He, C., Mehrmann, V. 30 October 1998 (has links)
A perturbation analysis shows that if a numerically stable
procedure is used to compute the matrix sign function, then it is competitive
with conventional methods for computing invariant subspaces.
Stability analysis of the Newton iteration improves an earlier result of Byers
and confirms that ill-conditioned iterates may cause numerical
instability. Numerical examples demonstrate the theoretical results.
|
10 |
Solving Linear Matrix Equations via Rational Iterative SchemesBenner, Peter, Quintana-Ortí, Enrique, Quintana-Ortí, Gregorio 01 September 2006 (has links)
We investigate the numerical solution of stable Sylvester equations via iterative schemes proposed for computing the sign function of a matrix. In particular, we discuss how the rational iterations for the matrix sign function can efficiently be adapted to the special structure implied by the Sylvester equation. For Sylvester equations with factored constant term as those arising in model reduction or image restoration, we derive an algorithm that computes the solution in factored form directly. We also suggest convergence criteria for the resulting iterations and compare the accuracy and performance of the resulting methods with existing Sylvester solvers. The algorithms proposed here are easy to parallelize. We report on the parallelization of those algorithms and demonstrate their high efficiency and scalability using experimental results obtained on a cluster of Intel Pentium Xeon processors.
|
Page generated in 0.0832 seconds