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

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Abstract

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.

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Authors and Affiliations

  1. School of Mathematical Sciences, Xiamen University, Shi Ming Nan Road, No. 422, Xiamen, Fujian, 361005, P.R. China

    Yunkun Chen

  2. School of Mathematics and Computer Science, Guizhou Normal University, Bao Shan Bei Road, No. 116, Guiyang, Guizhou, 550001, P. R. China

    Yunkun Chen

  3. School of Mathematical Sciences, Fudan University, Handan Road, No. 220, Shanghai, 200433, P.R. China

    Xinghua Shi & Yimin Wei

  4. Shanghai Key Laboratory of Contemporary Applied Mathematics, Handan Road, No. 220, Shanghai, 200433, P. R. China

    Yimin Wei

Authors
  1. Yunkun Chen
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  2. Xinghua Shi
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  3. Yimin Wei
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Correspondence to Yunkun Chen.

Additional information

In memory of Professor Miroslav Fiedler

The research has been supported by the National Natural Science Foundation of China under grant 11271084.

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Chen, Y., Shi, X. & Wei, Y. Convergence of Rump’s method for computing the Moore-Penrose inverse. Czech Math J 66, 859–879 (2016). https://doi.org/10.1007/s10587-016-0297-3

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  • DOI: https://doi.org/10.1007/s10587-016-0297-3

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