Iterative refinement techniques for solving block linear systems of equations

Agata Smoktunowicz; Alicja Smoktunowicz

doi:10.1016/j.apnum.2011.11.004

Iterative refinement techniques for solving block linear systems of equations

Agata Smoktunowicz, Alicja Smoktunowicz^*

^*Corresponding author for this work

School of Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract / Description of output

We study the numerical properties of classical iterative refinement (IR) and k-fold iterative refinement (RIR) for computing the solution of a nonsingular linear system of equations Ax = b with A partitioned into blocks using floating point arithmetic. We assume that all computations are performed in the working (fixed) precision. We prove that the numerical quality of RIR is superior to that of IR.

Original language	English
Pages (from-to)	220-229
Number of pages	10
Journal	Applied Numerical Mathematics
Volume	67
DOIs	https://doi.org/10.1016/j.apnum.2011.11.004
Publication status	Published - May 2013

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10.1016/j.apnum.2011.11.004

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title = "Iterative refinement techniques for solving block linear systems of equations",

abstract = "We study the numerical properties of classical iterative refinement (IR) and k-fold iterative refinement (RIR) for computing the solution of a nonsingular linear system of equations Ax = b with A partitioned into blocks using floating point arithmetic. We assume that all computations are performed in the working (fixed) precision. We prove that the numerical quality of RIR is superior to that of IR.",

author = "Agata Smoktunowicz and Alicja Smoktunowicz",

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AU - Smoktunowicz, Alicja

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AB - We study the numerical properties of classical iterative refinement (IR) and k-fold iterative refinement (RIR) for computing the solution of a nonsingular linear system of equations Ax = b with A partitioned into blocks using floating point arithmetic. We assume that all computations are performed in the working (fixed) precision. We prove that the numerical quality of RIR is superior to that of IR.

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DO - 10.1016/j.apnum.2011.11.004

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JO - Applied Numerical Mathematics

JF - Applied Numerical Mathematics

ER -

Iterative refinement techniques for solving block linear systems of equations

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Nil algebras, algebraic algebras and algebras with finite Gelfand-Kirillov dimension

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Iterative refinement techniques for solving block linear systems of equations

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Nil algebras, algebraic algebras and algebras with finite Gelfand-Kirillov dimension

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