2023
DOI: 10.48550/arxiv.2303.04251
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Optimal Solutions of Well-Posed Linear Systems via Low-Precision Right-Preconditioned GMRES with Forward and Backward Stabilization

Abstract: In scientific applications, linear systems are typically well-posed, and yet the coefficient matrices may be nearly singular in that the condition number κ(A) may be close to 1/εw, where εw denotes the unit roundoff of the working precision. Accurate and efficient solutions to such systems pose daunting challenges. It is well known that iterative refinement (IR) can make the forward error independent of κ(A) if κ(A) is sufficiently smaller than 1/εw and the residual is computed in higher precision. Recently, C… Show more

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