关于一类特殊 3 × 3 块鞍点系统解的结构向后误差分析
Structured Backward Error Analysis ona Special Class of Block Three-by-ThreeSaddle Point Systems
DOI: 10.12677/PM.2023.135155, PDF, HTML, 下载: 165  浏览: 245  科研立项经费支持
作者: 邢嘉璐：西北师范大学，数学与统计学院，甘肃 兰州
关键词: 3 × 3 块鞍点问题；向后误差；结构向后误差；Block 3 × 3 Saddle Point Problem； Backward Error； Structured Backward Error
摘要: 近年来，一类特殊的 3 × 3 块鞍点系统被广泛应用于一些物理问题中。 为了便于测试实际数值算法的稳定性，本文对这种类型的 3 × 3 块鞍点系统进行了结构向后误差分析，并给出了结构向后误差的可计算的具体公式。 基于结构向后误差，我们进行了数值实验。 数值实验结果表明该表达式可用于检验实际算法的稳定性。
Abstract: In recent years, a special class of block three-by-three saddle point systems is widely applied to a number of physical problems. In order to evaluate the stability of actual numerical algorithms, this paper performs the structured backward error analysis for this type of block three-by-three saddle point system and presents an explicit and computable formula for the structured backward error. Based on the structured backward error, we perform numerical experiment. Numerical example shows that the expressions are useful for testing the stability of practical algorithms.
文章引用：邢嘉璐. 关于一类特殊 3 × 3 块鞍点系统解的结构向后误差分析[J]. 理论数学, 2023, 13(5): 1528-1547. https://doi.org/10.12677/PM.2023.135155

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