Print Email Facebook Twitter Induced Dimension Reduction algorithms for solving non-symmetric sparse matrix problems Title Induced Dimension Reduction algorithms for solving non-symmetric sparse matrix problems Author Astudillo Rengifo, R.A. (TU Delft Numerical Analysis) Contributor Vuik, Cornelis (promotor) van Gijzen, M.B. (copromotor) Degree granting institution Delft University of Technology Date 2018-03-16 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 thiskind of problems. In particular, when the matrices involved are sparse andnon-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 standardeigenvalue 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. Subject Krylov subspace methodsInduced Dimension Reductionsystem of linear equationseigenvalues/eigenvectors approximationsolution of matrix linear problems To reference this document use: https://doi.org/10.4233/uuid:85261582-62d7-4b17-9c18-a1b2d11a07b6 ISBN 978-94-6366-019-8 Part of collection Institutional Repository Document type doctoral thesis Rights © 2018 R.A. Astudillo Rengifo Files PDF ra_dissertation.pdf 2.58 MB Close viewer /islandora/object/uuid:85261582-62d7-4b17-9c18-a1b2d11a07b6/datastream/OBJ/view