Induced Dimension Reduction Method for Solving Linear Matrix Equations

Astudillo Rengifo, R.A.; van Gijzen, M.B.

doi:10.1016/j.procs.2016.05.313

Induced Dimension Reduction Method for Solving Linear Matrix Equations

Title

Induced Dimension Reduction Method for Solving Linear Matrix Equations

Author

Astudillo Rengifo, R.A. (TU Delft Numerical Analysis)
van Gijzen, M.B. (TU Delft Numerical Analysis)

Date

2016

Abstract

This paper discusses the solution of large-scale linear matrix equations using the Induced Dimension reduction method (IDR(s)). IDR(s) was originally presented to solve system of linear equations, and is based on the IDR(s) theorem. We generalize the IDR(s) theorem to solve linear problems in any finite-dimensional space. This generalization allows us to develop IDR(s) algorithms to approximate the solution of linear matrix equations. The IDR(s) method presented here has two main advantages; firstly, it does not require the computation of inverses of any matrix, and secondly, it allows incorporation of preconditioners. Additionally, we present a simple preconditioner to solve the Sylvester equation based on a fixed point iteration. Several numerical examples illustrate the performance of IDR(s) for solving linear matrix equations. We also present the software implementation.

Subject

Matrix linear equations
Krylov subspace methods
Dimension Reduction method
Preconditioner
Numerical software

To reference this document use:

http://resolver.tudelft.nl/uuid:6ec91b16-0cac-4894-b1a0-28f2ca5404e7

DOI

https://doi.org/10.1016/j.procs.2016.05.313

ISSN

1877-0509

Source

Procedia Computer Science, 80, 222-232

Part of collection

Institutional Repository