Probabilistic error analysis of gaussian elimination in floating point and logarithmic arithmetic

J. L. Barlow; E. H. Bareiss

doi:10.1007/bf02251834

Probabilistic error analysis of gaussian elimination in floating point and logarithmic arithmetic

Computing ◽

10.1007/bf02251834 ◽

1985 ◽

Vol 34 (4) ◽

pp. 349-364 ◽

Cited By ~ 7

Author(s):

J. L. Barlow ◽

E. H. Bareiss

Keyword(s):

Error Analysis ◽

Gaussian Elimination ◽

Floating Point ◽

Probabilistic Error

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Error Analysis on Floating-Point Arithmetic in C Programming Language Library Functions

2013 Fourth International Conference on Emerging Intelligent Data and Web Technologies ◽

10.1109/eidwt.2013.134 ◽

2013 ◽

Author(s):

Min Tang ◽

Xia Zeng ◽

Kai Song ◽

Jian Liu

Keyword(s):

Error Analysis ◽

Programming Language ◽

Floating Point ◽

C Programming Language ◽

Floating Point Arithmetic ◽

C Programming ◽

Point Arithmetic

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Probabilistic Error Analysis of Approximate Adders and Multipliers

Approximate Circuits ◽

10.1007/978-3-319-99322-5_5 ◽

2018 ◽

pp. 99-120 ◽

Cited By ~ 2

Author(s):

Sana Mazahir ◽

Muhammad Kamran Ayub ◽

Osman Hasan ◽

Muhammad Shafique

Keyword(s):

Error Analysis ◽

Probabilistic Error

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COMPONENT-WISE ERROR ANALYSIS OF ITERATIVE METHODS PRACTICED ON A FLOATING-POINT SYSTEM

Memoirs of the Faculty of Science Kyushu University Series A Mathematics ◽

10.2206/kyushumfs.27.23 ◽

1973 ◽

Vol 27 (1) ◽

pp. 23-64 ◽

Cited By ~ 5

Author(s):

Minoru URABE

Keyword(s):

Error Analysis ◽

Iterative Methods ◽

Floating Point ◽

Point System

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A Note on the Perturbation of arithmetic expressions

Baghdad Science Journal ◽

10.21123/bsj.13.1.190-197 ◽

2016 ◽

Vol 13 (1) ◽

pp. 190-197

Author(s):

Baghdad Science Journal

Keyword(s):

Error Analysis ◽

Gaussian Elimination ◽

Effective Means ◽

Numerical Algorithms ◽

Posteriori Error ◽

Condition Numbers ◽

A Posteriori ◽

Rounding Errors ◽

A Posteriori Error ◽

Forward Error

In this paper we present the theoretical foundation of forward error analysis of numerical algorithms under;• Approximations in "built-in" functions.• Rounding errors in arithmetic floating-point operations.• Perturbations of data.The error analysis is based on linearization method. The fundamental tools of the forward error analysis are system of linear absolute and relative a prior and a posteriori error equations and associated condition numbers constituting optimal of possible cumulative round – off errors. The condition numbers enable simple general, quantitative bounds definitions of numerical stability. The theoretical results have been applied a Gaussian elimination, and have proved to be very effective means of both a priori and a posteriori error analysis.

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