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Highly accurate verified error bounds for Krylov type linear system solvers

Authors
Journal
Applied Numerical Mathematics
0168-9274
Publisher
Elsevier
Publication Date
Volume
45
Issue
1
Identifiers
DOI: 10.1016/s0168-9274(02)00234-9
Keywords
  • Large Sparse Linear Systems Of Equations
  • Preconditioner
  • Krylov Methods
  • Verification
Disciplines
  • Mathematics

Abstract

Abstract Preconditioned Krylov subspace solvers are an important and frequently used technique for solving large sparse linear systems. There are many advantageous properties concerning convergence rates and error estimates. However, implementing such a solver on a computer, we often observe an unexpected and even contrary behavior. The purpose of this paper is to show that this gap between the theoretical and practical behavior can be narrowed by using a problem-oriented arithmetic. In addition we give rigorous error bounds to our computed results.

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