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An efficient method to compute different types of generalized inverses based on linear transformation

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  • Ma, Jie
  • Gao, Feng
  • Li, Yongshu

Abstract

In this paper, we present functional definitions of all types of generalized inverses related to the {1}-inverse, which is a continuation of the work of Campbell and Meyer (2009). According to these functional definitions, we further derive novel representations for all types of generalized inverses related to the {1}-inverse in terms of the bases for R(A*), N(A) and N(A*). Based on these representations, we present the corresponding algorithm for computing various generalized inverses related to the {1}-inverse of a matrix and analyze the computational complexity of our algorithm for a constant matrix. Finally, we implement our algorithm and several known algorithms for symbolic computation of the Moore-–Penrose inverse in the symbolic computational package MATHEMATICA and compare their running times. Numerical experiments show that our algorithm outperforms these known algorithms when applied to compute the Moore–Penrose inverse of one-variable rational matrices, but is not the best choice for two-variable rational matrices in practice.

Suggested Citation

  • Ma, Jie & Gao, Feng & Li, Yongshu, 2019. "An efficient method to compute different types of generalized inverses based on linear transformation," Applied Mathematics and Computation, Elsevier, vol. 349(C), pages 367-380.
    • Handle: RePEc:eee:apmaco:v:349:y:2019:i:c:p:367-380
    DOI: 10.1016/j.amc.2018.12.064
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    References listed on IDEAS

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    1. Xingping Sheng, 2014. "Execute Elementary Row and Column Operations on the Partitioned Matrix to Compute M-P Inverse," Abstract and Applied Analysis, Hindawi, vol. 2014, pages 1-6, March.
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    Cited by:

    1. Dilan Ahmed & Mudhafar Hama & Karwan Hama Faraj Jwamer & Stanford Shateyi, 2019. "A Seventh-Order Scheme for Computing the Generalized Drazin Inverse," Mathematics, MDPI, vol. 7(7), pages 1-10, July.

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