New Upper Bounds for the Inverse of $H$-Matrices Including $S$-SDD Matrices and Linear Complementarity Problems
Received:March 17, 2023  Revised:July 08, 2023
Key Words: linear complementarity problem   error bound   upper bound   $S$-SDD matrices   $H$-matrices  
Fund Project:Supported by the Scientific Research Project of Education Department of Hunan Province (Grant No.21C0837).
Author NameAffiliation
Yebo XIONG Department of Mathematics and Statistics, Hunan First Normal University, Hunan 410205, P. R. China 
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      A partition reduction method is used to obtain new upper bounds for the inverses of $H$-matrices and $S$-strictly diagonally dominant ($S$-SDD) matrices. The estimates are expressed via the determinants of third order matrices. Numerical experiments with various random matrices show that they are stable and better than the estimates presented in literatures. We use these upper bounds to improve known error estimates for linear complementarity problems with $H$-matrices and $S$-SDD matrices.
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