Françoise Chatelin, Valérie Frayssé, Thierry Braconnier  Home/Search
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Abstract: It is known that finite precision versus exact computation is a crucial issue only when the computation takes place in the neighbourhood of a singularity. In such a situation, it is essential to know the distance to singularity. Much attention has been dedicated to the relationship between the distance to singularity ffi and the condition number K of the problem under study. The wellknown Turing theorem states that, for a linear system Ax = b, the distance to singularity, in a normwise... (Update)
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BibTeX entry: (Update)
F. Chatelin, V. Fraysse, and T. Braconnier, Computations in the neighbourhood of algebraic singularities, Numer. Funct. Anal. and Optimiz., 16(3&4) (1995), pp. 287--302. http://citeseer.ist.psu.edu/chatelin95computations.html More
@misc{ chatelin95computations,
author = "F. Chatelin and V. Fraysse and T. Braconnier",
title = "Computations in the neighbourhood of algebraic singularities",
text = "F. Chatelin, V. Fraysse, and T. Braconnier, Computations in the neighbourhood
of algebraic singularities, Numer. Funct. Anal. and Optimiz., 16(3&4) (1995),
pp. 287--302.",
year = "1995",
url = "citeseer.ist.psu.edu/chatelin95computations.html" }
Citations (may not include all citations):117 Rounding errors in algebraic processes (context) - Wilkinson - 1963
41 Valeurs propres de matrices (context) - Chatelin
40 On condition numbers and the distance to the nearest ill-pos.. (context) - Demmel - 1987
18 Qualitative Computing: elements of a theory for finite preci.. (context) - Chatelin, Frayss'e - 1993
18 A collection of test matrices in MATLAB (context) - Higham - 1991
14 The componentwise distance to the nearest singular matrix (context) - Demmel - 1992
14 A contribution to the theory of condition (context) - Geurts - 1982
14 Complexity of Bezout's theorem (context) - Shub, Smale - 1992
9 A theory of condition (context) - Rice - 1966
5 Etude statistique de la qualit'e num'erique et arithm'etique.. (context) - Chatelin
4 Nearest defective matrices and the geometry of illconditioni.. (context) - Demmel - 1990
4 Non singularity under data rounding (context) - Rohn - 1990
4 Elements of a condition theory for the computational analysi.. (context) - Chatelin, Frayss'e - 1992
3 Reliability of computer solutions (context) - Frayss'e - 1992
3 R'esolution approch'ee d (context) - Chatelin - 1989
[Article contains additional citations not shown here]
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