Induced Dimension Reduction algorithms for solving non-symmetric sparse matrix problems

Doctoral thesis (2018)

Authors

R.A. Astudillo Rengifo Numerical Analysis - EEMCS
Research Group
Numerical Analysis (EEMCS) (TU Delft)
Copyright: © 2018 R.A. Astudillo Rengifo
DOI
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https://doi.org/10.4233/uuid:85261582-62d7-4b17-9c18-a1b2d11a07b6
Krylov subspace methods Induced Dimension Reduction System of linear equations Eigenvalues/eigenvectors approximation Solution of matrix linear problems
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Published Date

2018

Language

English

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Faculty

Electrical Engineering, Mathematics and Computer Science

Department

Delft Institute of Applied Mathematics

Research Group

Numerical Analysis

Abstract

In several applications in science and engineering, different types of matrix problems emerge from the discretization of partial differential equations.
This thesis is devoted to the development of new algorithms to solve this
kind of problems. In particular, when the matrices involved are sparse and
non-symmetric. The new algorithms are based on the Induced Dimension Reduction method [IDR(s)].
IDR(s) is a Krylov subspace method originally proposed in 2008 to solve systems of linear equations. IDR(s) has received considerable attention due to its stable and fast convergence. It is, therefore, natural to ask if it is possible to extend IDR(s) to solve other matrix problems, and if so, to compare those extensions with other well-established methods. This work aims to answer these questions.
The main matrix problems considered in this dissertation are: the standard
eigenvalue problem, the quadratic eigenvalue problem, the solution of systems of linear equations, the solution of sequences of systems of linear equations, and linear matrix equations. We focus on examples that arise from the discretization of partial differential equations.