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Title:Efficient projection space updates for the approximation of iterative solutions to linear systems with successive right hand sides
Author(s):Christensen, Nicholas
Advisor(s):Fischer, Paul F.
Department / Program:Computer Science
Discipline:Computer Science
Degree Granting Institution:University of Illinois at Urbana-Champaign
Degree:M.S.
Genre:Thesis
Subject(s):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
Abstract: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.
Issue Date:2017-12-11
Type:Text
URI:http://hdl.handle.net/2142/99410
Rights Information: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
Date Available in IDEALS:2018-03-13
Date Deposited:2017-12


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