Nonlinear Theory and Its Applications, IEICE
Online ISSN : 2185-4106
ISSN-L : 2185-4106
Special Section on Recent Progress in Verified Numerical Computations
Backward error bounds for 2×2 linear systems arising in the diagonal pivoting method
Kenta KobayashiTakeshi Ogita
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2015 Volume 6 Issue 3 Pages 383-390

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Abstract

Matrix factorizations such as LU, Cholesky and others are widely used for solving linear systems. In particular, the diagonal pivoting method can be applied to symmetric and indefinite matrices. Floating-point arithmetic is extensively used for this purpose. Since finite precision numbers are treated, rounding errors are involved in computed results. In this paper rigorous backward error bounds for 2×2 linear systems which arise in the factorization process of the diagonal pivoting method are given. These bounds are much better than previously known ones.

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© 2015 The Institute of Electronics, Information and Communication Engineers
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