Convergence of Rump's method for computing the Moore-Penrose inverse

Czechoslovak Mathematical Journal

Xinghua Shi¹  Yimin Wei²  Yunkun Chen³ 

[1] School of Mathematical Sciences, Fudan University, Handan Road, No. 220, Shanghai, 200433, P. R. China;School of Mathematical Sciences, Fudan University, Handan Road, No. 220, Shanghai, 200433, P. R. China, and Shanghai Key Laboratory of Contemporary Applied Mathematics, Handan Road, No. 220, Shanghai, 200433, P. R. China.;School of Mathematical Sciences, Xiamen University, Shi Ming Nan Road, No. 422, Xiamen 361005, Fujian, P. R. China, and School of Mathematics and Computer Science, Guizhou Normal University, Bao Shan Bei Road, No. 116, Guiyang 550001, Guizhou, P. R. China

关键词: Moore-Penrose inverse;    condition number;    ill-conditioned matrix;   

DOI  :  

学科分类：数学（综合）

来源: Akademie Ved Ceske Republiky

【 摘 要 】

We extend Rump's verified method (S. Oishi, K. Tanabe, T. Ogita, S. M. Rump (2007)) for computing the inverse of extremely ill-conditioned square matrices to computing the Moore-Penrose inverse of extremely ill-conditioned rectangular matrices with full column (row) rank. We establish the convergence of our numerical verified method for computing the Moore-Penrose inverse. We also discuss the rank-deficient case and test some ill-conditioned examples. We provide our Matlab codes for computing the Moore-Penrose inverse.

【 授权许可】

Unknown