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Journal Articles Numerical Linear Algebra with Applications Year : 2021

Minimizing convex quadratics with variable precision conjugate gradients

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Abstract

We investigate the method of conjugate gradients, exploiting inac-curate matrix-vector products, for the solution of convex quadratic op-timization problems. Theoretical performance bounds are derived, andthe necessary quantities occurring in the theoretical bounds estimated,leading to a practical algorithm. Numerical experiments suggest thatthis approach has significant potential, including in the steadily moreimportant context of multi-precision computations.

Dates and versions

hal-02959082 , version 1 (06-10-2020)

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Serge Gratton, Ehouarn Simon, David Titley-Peloquin, Philippe Toint. Minimizing convex quadratics with variable precision conjugate gradients. Numerical Linear Algebra with Applications, 2021, 28 (e2337). ⟨hal-02959082⟩
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