Backward error bounds for 2&times;2 linear systems arising in the diagonal pivoting method

Kenta Kobayashi; Takeshi Ogita

doi:10.1587/nolta.6.383

Backward error bounds for 2×2 linear systems arising in the diagonal pivoting method

Nonlinear Theory and Its Applications IEICE ◽

10.1587/nolta.6.383 ◽

2015 ◽

Vol 6 (3) ◽

pp. 383-390

Author(s):

Kenta Kobayashi ◽

Takeshi Ogita

Keyword(s):

Linear Systems ◽

Error Bounds ◽

Backward Error

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Verified Error Bounds for Linear Systems Through the Lanczos Process

Developments in Reliable Computing ◽

10.1007/978-94-017-1247-7_20 ◽

1999 ◽

pp. 255-267

Author(s):

Andreas Frommer ◽

Andre Weinberg

Keyword(s):

Linear Systems ◽

Error Bounds ◽

Lanczos Process

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Improved componentwise verified error bounds for least squares problems and underdetermined linear systems

Numerical Algorithms ◽

10.1007/s11075-013-9735-6 ◽

2013 ◽

Vol 66 (2) ◽

pp. 309-322 ◽

Cited By ~ 5

Author(s):

Siegfried M. Rump

Keyword(s):

Least Squares ◽

Linear Systems ◽

Error Bounds ◽

Least Squares Problems ◽

Underdetermined Linear Systems

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Backward error analysis for linear systems associated with inverses ofH-matrices

BIT Numerical Mathematics ◽

10.1007/bf01934520 ◽

1984 ◽

Vol 24 (1) ◽

pp. 102-112 ◽

Cited By ~ 5

Author(s):

M. Neumann ◽

R. J. Plemmons

Keyword(s):

Error Analysis ◽

Linear Systems ◽

Backward Error Analysis ◽

Backward Error

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On the Symmetric Componentwise Relative Backward Error for Linear Systems of Equations

SIAM Journal on Matrix Analysis and Applications ◽

10.1137/140986566 ◽

2017 ◽

Vol 38 (4) ◽

pp. 1100-1115 ◽

Cited By ~ 1

Author(s):

Stanley C. Eisenstat ◽

Serge Gratton ◽

David Titley-Peloquin

Keyword(s):

Linear Systems ◽

Systems Of Equations ◽

Backward Error ◽

Linear Systems Of Equations

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Backward error bounds for approximate Krylov subspaces

Linear Algebra and its Applications ◽

10.1016/s0024-3795(01)00413-x ◽

2002 ◽

Vol 340 (1-3) ◽

pp. 81-86 ◽

Cited By ~ 7

Author(s):

G.W. Stewart

Keyword(s):

Error Bounds ◽

Krylov Subspaces ◽

Backward Error

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Backward Error Bounds of Block LDLT factorizations

IEICE Proceeding Series ◽

10.15248/proc.1.876 ◽

2014 ◽

Vol 1 ◽

pp. 876-876

Author(s):

Takeshi Ogita

Keyword(s):

Error Bounds ◽

Backward Error

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Backward error analysis for totally positive linear systems

Numerische Mathematik ◽

10.1007/bf01399609 ◽

1976 ◽

Vol 27 (4) ◽

pp. 485-490 ◽

Cited By ~ 61

Author(s):

Carl de Boor ◽

Allan Pinkus

Keyword(s):

Error Analysis ◽

Linear Systems ◽

Backward Error Analysis ◽

Backward Error ◽

Totally Positive

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Sharp error bounds of some Krylov subspace methods for non-Hermitian linear systems

Applied Mathematics and Computation ◽

10.1016/s0096-3003(99)00027-2 ◽

2000 ◽

Vol 109 (2-3) ◽

pp. 273-285 ◽

Cited By ~ 16

Author(s):

Zhong-Zhi Bai

Keyword(s):

Linear Systems ◽

Error Bounds ◽

Krylov Subspace ◽

Krylov Subspace Methods ◽

Subspace Methods ◽

Sharp Error

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Backward error bounds for polynomial eigenvalue problem solved by a Rayleigh–Ritz type contour integral-based eigensolver

Applied Mathematics Letters ◽

10.1016/j.aml.2019.106122 ◽

2020 ◽

Vol 102 ◽

pp. 106122

Author(s):

Hongjia Chen ◽

Lei Du

Keyword(s):

Eigenvalue Problem ◽

Error Bounds ◽

Contour Integral ◽

Backward Error ◽

Polynomial Eigenvalue Problem

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Computing Error Bounds in Solving Linear Systems

Mathematics of Computation ◽

10.2307/2004052 ◽

1962 ◽

Vol 16 (79) ◽

pp. 323 ◽

Cited By ~ 12

Author(s):

J. Schroder

Keyword(s):

Linear Systems ◽

Error Bounds ◽

Computing Error

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