Results 271 to 280 of about 1,028,403 (287)

A consideration on the condition number of extremely ill-conditioned matrices

2013 European Conference on Circuit Theory and Design (ECCTD), 2013
As for a matrix A we examine two problems: (a) To find the upper and the lower bound of Cond2(A) in terms of two coefficients p1 and pn-1 (see Section 2) of the characteristic polynomial of AA T, and (b) proof of existence of a matrix A having considerably larger condition number than that obtained in the previous papers. The connection between (a) and
Tetsuo Nishi, Siegfried M. Rump, Shin'ichi Oishi   +2 more
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A CONDITIONAL DENSITY FOR CARMICHAEL NUMBERS

Bulletin of the Australian Mathematical Society, 2020
Under sufficiently strong assumptions about the first prime in an arithmetic progression, we prove that the number of Carmichael numbers up to$X$is$\gg X^{1-R}$, where$R=(2+o(1))\log \log \log \log X/\text{log}\log \log X$. This is close to Pomerance’s conjectured density of$X^{1-R}$with$R=(1+o(1))\log \log \log X/\text{log}\log X$.
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Condition numbers and D-efficiency

Statistics & Probability Letters, 2004
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On computing condition numbers for the nonsymmetric eigenproblem

ACM Transactions on Mathematical Software, 1993
We review the theory of condition numbers for the nonsymmetric eigenproblem and give a tabular summary of bounds for eigenvalues, means of clusters of eigenvalues, eigenvectors, invariant subspaces, and related quantities. We describe the design of new algorithms for estimating these condition numbers.
Zhaojun Bai, James Demmel, A. McKenney
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Probabilistic analyses of condition numbers

Acta Numerica, 2016
In recent decades, condition numbers have joined forces with probabilistic analysis to give rise to a form of condition-based analysis of algorithms. In this paper we survey how this analysis is done via a number of examples. We precede this catalogue of examples with short primers on both condition numbers and probabilistic analyses.
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Probabilistic analysis of condition numbers

Proceedings of the 36th international symposium on Symbolic and algebraic computation, 2011
Condition numbers are well known in numerical linear algebra. It is less known that this concept also plays a crucial part in understanding the efficiency of algorithms in linear programming, convex optimization, and for solving systems of polynomial equations. Indeed, the running time of such algorithms may be often effectively bounded in terms of the
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On Condition Number Theorems in Mathematical Programming

Journal of Optimization Theory and Applications, 2017
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Nonnormality and Jordan Condition Numbers of Matrices

Journal of the ACM, 1969
A lower bound for the departure from normality of an n X n matrix A is given. Furthermore, various inequalities are obtained for certain condition numbers associated with the reduction of A to its Jordan canonical form.
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Condition Numbers

2000
Albrecht Böttcher, Sergei M. Grudsky
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Condition number

2001
Saul I. Gass, Carl M. Harris
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