Efficient projection space updates for the approximation of iterative solutions to linear systems with successive right hand sides
Christensen, Nicholas
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https://hdl.handle.net/2142/99410
Description
Title
Efficient projection space updates for the approximation of iterative solutions to linear systems with successive right hand sides
Author(s)
Christensen, Nicholas
Issue Date
2017-12-11
Director of Research (if dissertation) or Advisor (if thesis)
Fischer, Paul F.
Department of Study
Computer Science
Discipline
Computer Science
Degree Granting Institution
University of Illinois at Urbana-Champaign
Degree Name
M.S.
Degree Level
Thesis
Keyword(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.
Graduation Semester
2017-12
Type of Resource
text
Permalink
http://hdl.handle.net/2142/99410
Copyright and License 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.
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