Abstract In this report we show that the iterated regularization scheme due to Riley and Golub, sometimes also called the iterated Tikhonov regularization, can be generalized to damped least squares problems where the weights matrix D is not necessarily the identity but a general symmetric and positive definite matrix. We show that the iterative scheme approaches the same point as the unique solutions of the regularized problem, when the regularization parameter goes to 0. Furthermore this point can be characterized as the solution of a weighted minimum Euclidean norm problem. Finally several numerical experiments were performed in the field of rigid multibody dynamics supporting the theoretical claims.

中文翻译：

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加权线性最小二乘问题的迭代求解

摘要 在本报告中，我们展示了由于 Riley 和 Golub 的迭代正则化方案，有时也称为迭代 Tikhonov 正则化，可以推广到阻尼最小二乘问题，其中权重矩阵 D 不一定是单位，而是一般对称和正定矩阵。我们表明，当正则化参数变为 0 时，迭代方案接近与正则化问题的唯一解相同的点。此外，这一点可以表征为加权最小欧几里得范数问题的解。最后，在支持理论主张的刚性多体动力学领域进行了几次数值实验。