Minimizing convex quadratic with variable precision conjugate gradients
This work provides a practical method for reducing computational cost in convex quadratic optimization by leveraging variable precision, which is increasingly relevant for multi-precision hardware.
The authors develop a practical conjugate gradient algorithm that uses variable-precision matrix-vector products to solve convex quadratic optimization problems, demonstrating significant potential in multi-precision computations through numerical experiments.
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