A Monotonicity Result for Norms in Conjugate Gradient Algorithms

被引：0
|
作者：
Anton Schiela
机构：
[1] Universität Bayreuth,
来源：
Journal of Optimization Theory and Applications | 2023年 / 196卷
关键词：
Conjugate gradients; Quadratic optimization; Monotonicity of norms; 90C06; 65J10; 90C48;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
We show a monotonicity result, enjoyed by norms of iterates of the cg method. It relates the energy norm and the norm, induced by the preconditioner. We place this result into the context of known results and sketch possible applications to ill-posed problems and in unconstrained optimization. Finally, we give some illustration by a numerical example.
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页码：126 / 146
页数：20
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