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Condition number of Bott–Duffin inverse and their condition numbers
Applied Mathematics and Computation, 2003The paper studies the normwise relative condition number of the Bott-Duffin inverse and the corresponding condition number for the constrained linear systems \(Ax+y=b,x\in L,y\in L^{\bot }\). Since the condition number cannot be computed exactly, the authors consider the sensitivity of the problem ``the condition number of the condition number'' by ...
Yimin Wei 0001, Wei Xu
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2016
In the following chapter we are going to discuss the solution of a system of linear equations $$\displaystyle{ Ax = b }$$ (2.1) where A is an n × n real matrix: \(A \in \mathbb{R}^{n\times n},\,b \in \mathbb{R}^{n}\) is a given vector and \(x \in \mathbb{R}^{n}\) is the unknown vector.
Gisbert Stoyan, Agnes Baran
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In the following chapter we are going to discuss the solution of a system of linear equations $$\displaystyle{ Ax = b }$$ (2.1) where A is an n × n real matrix: \(A \in \mathbb{R}^{n\times n},\,b \in \mathbb{R}^{n}\) is a given vector and \(x \in \mathbb{R}^{n}\) is the unknown vector.
Gisbert Stoyan, Agnes Baran
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Condition number of Drazin inverse and their condition numbers of singular linear systems
Applied Mathematics and Computation, 2003Various condition numbers are given for the Drazin inverse of a singular square matrix and for singular linear systems.
Yimin Wei 0001 +2 more
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Condition Number Theorems in Optimization
SIAM Journal on Optimization, 2003Summary: Condition numbers for optimization problems in Banach spaces are considered. Lower and upper estimates of the (suitably defined) distance from ill-conditioning are obtained in terms of the reciprocal of condition numbers. An approach is presented based on the metric regularity of the inverse to the arg min map.
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Applied Mathematics and Computation, 2008
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Jueping Chen, Zhaoliang Xu
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zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Jueping Chen, Zhaoliang Xu
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An Estimate for the Condition Number of a Matrix
SIAM Journal on Numerical Analysis, 1979It is important in practice when solving linear systems to have an economical method for estimating the condition number $\kappa (A)$ of the matrix of coefficients. An algorithm involving $O(n^2 )$ arithmetic operations is described; it gives a reliable indication of the order of magnitude of $\kappa (A)$.
Cline, A. K. +3 more
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A consideration on the condition number of extremely ill-conditioned matrices
2013 European Conference on Circuit Theory and Design (ECCTD), 2013As 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 +2 more
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A CONDITIONAL DENSITY FOR CARMICHAEL NUMBERS
Bulletin of the Australian Mathematical Society, 2020Under 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, 2004zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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On computing condition numbers for the nonsymmetric eigenproblem
ACM Transactions on Mathematical Software, 1993We 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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