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Perturbations of Moore-Penrose inverse and dual Moore-Penrose generalized inverse

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Abstract

In this paper, we present explicit expressions for the Moore-Penrose inverse of the perturbation matrix under the rank condition in the real field. Then we estimate the error between Moore-Penrose inverse and dual Moore-Penrose generalized inverse (DMPGI) and obtain an upper bound of the error. Furthermore, we discuss the above results under several special conditions.

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Funding

H. Wang is supported partially by Research Fund Project of Guangxi Minzu University under grant 2019KJQD03 and Thousands of Young and Middle-aged Key Teachers Training Programme in Guangxi Colleges and Universities under grant GUIJIAOSHIFAN2019-81HAO. Y. Wei is supported by Shanghai Municipal Science and Technology Commission under grant 23WZ2501400 and Ministry of Science and Technology of China under Grant G2023132005L.

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Authors and Affiliations

  1. Laboratory of Hybrid Computation and IC Design Analysis, Guangxi Minzu University, Nanning, 530006, People’s Republic of China

    Chong Cui & Hongxing Wang

  2. School of Mathematics Sciences and Shanghai Key Laboratory of Contemporary Applied Mathematics, Fudan University, Shanghai, 200433, People’s Republic of China

    Yimin Wei

Authors
  1. Chong Cui
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  2. Hongxing Wang
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  3. Yimin Wei
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Correspondence to Yimin Wei.

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Cui, C., Wang, H. & Wei, Y. Perturbations of Moore-Penrose inverse and dual Moore-Penrose generalized inverse. J. Appl. Math. Comput. 69, 4163–4186 (2023). https://doi.org/10.1007/s12190-023-01920-5

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