通过对称秩一更新计算矩阵的Moore-Penrose逆

Am. J. Comput. Math. Pub Date : 2011-09-19 DOI:10.4236/ajcm.2011.13016

Xuzhou Chen, J. Ji

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引用次数: 14

摘要

本文提出了一种计算矩阵a的Moore-Penrose逆的递归方法，该方法基于1阶修正矩阵的Moore-Penrose逆的表达式。分析了该方法的计算复杂度，并给出了一个数值算例。本文还提出了一种计算复杂度较低的算法。两种算法都在随机生成的矩阵上进行了测试。数值性能证实了我们的理论结果。

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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Computing the Moore-Penrose Inverse of a Matrix Through Symmetric Rank-One Updates

This paper presents a recursive procedure to compute the Moore-Penrose inverse of a matrix A. The method is based on the expression for the Moore-Penrose inverse of rank-one modified matrix. The computational complexity of the method is analyzed and a numerical example is included. A variant of the algorithm with lower computational complexity is also proposed. Both algorithms are tested on randomly generated matrices. Numerical performance confirms our theoretic results.

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Am. J. Comput. Math.

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