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 multiprecision computations.

中文翻译：

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用可变精度共轭梯度最小化凸二次方

我们研究共轭梯度的方法，利用不准确的矩阵向量乘积来解决凸二次优化问题。推导理论性能界限，并估计在理论界限内出现的必要数量，从而得出实用的算法。数值实验表明，这种方法具有巨大的潜力，包括在稳步提高的多精度计算环境中。