scholarly journals Computable backward error bounds for basic algorithms in linear algebra

2015 ◽  
Vol 6 (3) ◽  
pp. 360-363 ◽  
Author(s):  
Siegfried M. Rump
Keyword(s):  
Linear Algebra ◽  
Error Bounds ◽  
Backward Error

scholarly journals New error bounds for linear complementarity problems of Σ-SDD matrices and SB-matrices

2019 ◽  
Vol 17 (1) ◽  
pp. 1599-1614
Author(s):  
Zhiwu Hou ◽  
Xia Jing ◽  
Lei Gao
Keyword(s):  
Linear Algebra ◽  
Error Bound ◽  
Linear Complementarity Problem ◽  
Error Bounds ◽  
Complementarity Problems ◽  
Linear Complementarity Problems ◽  
Linear Complementarity ◽  
Numerical Examples ◽  
Numer Algor ◽  
Better Than

Abstract A new error bound for the linear complementarity problem (LCP) of Σ-SDD matrices is given, which depends only on the entries of the involved matrices. Numerical examples are given to show that the new bound is better than that provided by García-Esnaola and Peña [Linear Algebra Appl., 2013, 438, 1339–1446] in some cases. Based on the obtained results, we also give an error bound for the LCP of SB-matrices. It is proved that the new bound is sharper than that provided by Dai et al. [Numer. Algor., 2012, 61, 121–139] under certain assumptions.

Backward Error Bounds of Block LDLT factorizations

2014 ◽  
Vol 1 ◽  
pp. 876-876
Author(s):  
Takeshi Ogita
Keyword(s):  
Error Bounds ◽  
Backward Error

scholarly journals Improved Backward Error Bounds for LU and Cholesky Factorizations

2014 ◽  
Vol 35 (2) ◽  
pp. 684-698 ◽  
Author(s):  
Siegfried M. Rump ◽  
Claude-Pierre Jeannerod
Keyword(s):  
Error Bounds ◽  
Backward Error ◽  
Cholesky Factorizations
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