We derive bounds for the objective errors and gradient residuals when finding approximations to the solution of common regularized quadratic optimization problems within evolving Krylov spaces. These provide upper bounds on the number of iterations required to achieve a given stated accuracy. We illustrate the quality of our bounds on given test examples.

中文翻译：

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用于最小化正则二次子问题的迭代算法的误差估计

当找到正在发展的Krylov空间中常见正则二次优化问题的解的近似值时，我们得出目标误差和梯度残差的界限。这些为达到给定的精度要求的迭代次数提供了上限。我们在给定的测试示例上说明边界的质量。