Condition numbers and their condition numbers
نویسندگان
چکیده
منابع مشابه
NORTH- HOLLAND Condition Numbers and Their Condition Numbers
Various normwise relative condition numbers that measure the sensitivity of matrix inversion and the solution of linear systems are characterized. New results are derived for the cases where two common, noninduced matrix norms are used, and where different vector norms are used for the domain and range of the matrix. Condition numbers that respect the structure of symmetric problems are also an...
متن کاملCondition number of Bott-Duffin inverse and their condition numbers
Various normwise relative condition numbers that measure the sensitivity of Bott– Duffin inverse and the solution of constrained linear systems are characterized. The sensitivity of condition number itself is then investigated. Finally, upper bounds are derived for the sensitivity of componentwise condition numbers. 2002 Elsevier Science Inc. All rights reserved.
متن کاملCondition Numbers of Matrices
denote its Euclidean operator norm (often called the 2-norm). If is nonsingular, then its condition number () is defined by () = kk°°−1°° = 1() () where 1 ≥ 1 ≥ ≥ ≥ 0 are the singular values of . The s constitute lengths of the semi-axes of the hyperellipsoid = { : kk = 1} in -dimensional space; thus measures elongation of at its extreme [1]. The role that ...
متن کاملStructured Eigenvalue Condition Numbers
This paper investigates the effect of structure-preserving perturbations on the eigenvalues of linearly and nonlinearly structured eigenvalue problems. Particular attention is paid to structures that form Jordan algebras, Lie algebras, and automorphism groups of a scalar product. Bounds and computable expressions for structured eigenvalue condition numbers are derived for these classes of matri...
متن کاملOptimizing Condition Numbers
In this paper we study the problem of minimizing condition numbers over a compact convex subset of the cone of symmetric positive semidefinite n × n matrices. We show that the condition number is a Clarke regular strongly pseudoconvex function. We prove that a global solution of the problem can be approximated by an exact or an inexact solution of a nonsmooth convex program. This asymptotic ana...
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ژورنال
عنوان ژورنال: Linear Algebra and its Applications
سال: 1995
ISSN: 0024-3795
DOI: 10.1016/0024-3795(93)00066-9