Efficient projection space updates for the approximation of iterative solutions to linear systems with successive right hand sides

Accurate initial guesses to the solution can dramatically speed convergence of iterative solvers. In the case of successive right hand sides, it has been shown that accurate initial solutions may be obtained by projecting the newest right hand side vector onto a column space of recent prior solutions. We propose a technique to efficiently update the column space of prior solutions. We find this technique can modestly improve solver performance, though its potential is likely limited by the problem step size and the accuracy of the solver.

Name thesis:degree_name

M.S.

Level thesis:degree_level

Thesis

Discipline thesis:degree_discipline

Computer Science

Grantor

University of Illinois at Urbana-Champaign

Year dc:date

2018

Author dc:creator

• Christensen, Nicholas

Contributors dc:contributor

• Fischer, Paul F.

• Iterative solver
• Projection
• Solution approximation
• Ax = b
• Partial differential equations
• Linear system
• Oblique inner product
• Oblique QR factorization
• Updating QR factorization
• Successive right hand side
• Initial guess
• Reduced communication

Statement dc:rights

• This thesis is released into the public domain under the CC0 code. To the extent possible under law, the author waives all copyright and related or neighboring rights to this work.
• Copyright 2017 Nicholas Christensen

Language dc:language

en

Handle dc:identifier

http://hdl.handle.net/2142/99410

OAI identifier oai:identifier

oai:www.ideals.illinois.edu:2142/99410