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Schur Complement-Based Infinity Norm Bounds for the Inverse of DSDD Matrices

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Abstract

Based on the Schur complements, two upper bounds for the infinity norm of the inverse of doubly strictly diagonally dominant (DSDD) matrices are presented. As applications, an error bound for linear complementarity problems of DB-matrices and a lower bound for the smallest singular value of matrices are given.

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Acknowledgements

The author would like to thank Prof. Chaoqian Li and anonymous referees for their valuable suggestions. This work is supported by Natural Science Foundation of Guizhou Minzu University; Postgraduate Education Innovation Project of Guizhou Province (Grant No. YJSCXJH[2019]052).

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Authors and Affiliations

  1. College of Data Science and Information Engineering, Guizhou Minzu University, Guiyang, 550025, People’s Republic of China

    Caili Sang

  2. School of Mathematical Sciences, Guizhou Normal University, Guiyang, 550025, People’s Republic of China

    Caili Sang

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Correspondence to Caili Sang.

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Communicated by Mohammad S. Moslehian.

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Sang, C. Schur Complement-Based Infinity Norm Bounds for the Inverse of DSDD Matrices. Bull. Iran. Math. Soc. 47, 1379–1398 (2021). https://doi.org/10.1007/s41980-020-00447-w

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  • DOI: https://doi.org/10.1007/s41980-020-00447-w

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