Minimizing convex quadratic with variable precision conjugate gradients

TL;DR

This paper explores the use of variable precision conjugate gradients for efficiently solving convex quadratic problems, deriving theoretical bounds and demonstrating practical potential through numerical experiments, especially in multi-precision contexts.

Contribution

It introduces a practical algorithm leveraging inaccurate matrix-vector products in conjugate gradients, supported by theoretical bounds and numerical validation.

Findings

Significant potential shown in multi-precision computations

Theoretical performance bounds established

Numerical experiments confirm effectiveness

Abstract

We investigate the method of conjugate gradients, exploiting inaccurate matrix-vector products, for the solution of convex quadratic optimization problems. Theoretical performance bounds are derived, and the necessary quantities occurring in the theoretical bounds estimated, leading to a practical algorithm. Numerical experiments suggest that this approach has significant potential, including in the steadily more important context of multi-precision computations