On Rayleigh quotients and characteristic equations for symmetric matrices connected with coordinate updatings

IF 2.6 3区数学 Q2 MATHEMATICS, APPLIED

Advances in Computational Mathematics Pub Date : 2026-09-22 DOI:10.1007/s10444-026-10356-x

Zhong-Zhi Bai

引用次数: 0

Abstract

For the standard symmetric eigenvalue problem, with respect to the coordinate descent/updating method we reveal an intrinsic connection between the Rayleigh quotient and the characteristic equation, and show that the coordinate descent method and the coordinate updating method actually share the same structure and formulation. We then further formulate a general framework for these two iteration methods.

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关于坐标更新的对称矩阵的瑞利商和特征方程

对于标准对称特征值问题，通过坐标下降/更新方法揭示了瑞利商与特征方程之间的内在联系，并证明了坐标下降法与坐标更新法实际上具有相同的结构和公式。然后，我们进一步制定了这两种迭代方法的一般框架。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Advances in Computational Mathematics 数学-应用数学

CiteScore

3.00

自引率

5.90%

发文量

审稿时长

3 months

期刊介绍： Advances in Computational Mathematics publishes high quality, accessible and original articles at the forefront of computational and applied mathematics, with a clear potential for impact across the sciences. The journal emphasizes three core areas: approximation theory and computational geometry; numerical analysis, modelling and simulation; imaging, signal processing and data analysis. This journal welcomes papers that are accessible to a broad audience in the mathematical sciences and that show either an advance in computational methodology or a novel scientific application area, or both. Methods papers should rely on rigorous analysis and/or convincing numerical studies.