Results 241 to 250 of about 8,652,887 (279)

Probabilistic Estimation of Matrix Condition Number

Journal of Mathematical Sciences, 2020
Summary: Ill-conditioned matrices of systems of linear algebraic equations with random error of the right-hand side vector considered. The condition number \(\nu\) of the system matrix is investigated. It is shown that under some natural conditions the number \(\nu\) may be significantly decreased.
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Mixed, Componentwise, and Structured Condition Numbers

SIAM Journal on Matrix Analysis and Applications, 1993
The authors propose mixed and componentwise condition numbers for a general continuous map \(F\) at a point \(a\), and consider special cases when \(F\) is the map of the matrix inversion or of the solution of a linear system. Further they define structured condition numbers and give a detailed application to Vandermonde matrices.
Gohberg, I., Koltracht, I.
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Condition Number Theorems in Optimization

SIAM Journal on Optimization, 2003
Summary: 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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Arithmetical Conditions on Invariant Sylow Numbers

Mediterranean Journal of Mathematics, 2018
Let $G$ be a finite group and let $A$ be a subgroup of the automorphism group of $G$. Let $\pi(G)$ be the set of all prime divisors of $|G|$. For every $p\in \pi(G)$, define $ \nu_p^A(G)$ to be the number of Sylow $p$-subgroups of $G$ which are invariant under the action of $A$, and let $\mathrm{sn}_A(G)$ be the set of all values of $\nu_p^A(G)$ as $p$
Beltrán, Antonio, Shao, Changguo
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Unifying Condition Numbers for Linear Programming

Mathematics of Operations Research, 2003
In recent years, several condition numbers were defined for a variety of linear programming problems based upon relative distances to ill-posedness. In this paper, we provide a unifying view of some of these condition numbers. To do so, we introduce yet another linear programming problem and show that its distance to ill-posedness naturally captures ...
Cheung, Dennis, Cucker, Felipe, Peña, Javier   +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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Controllability Index Based on Conditioning Number

Journal of Dynamic Systems, Measurement, and Control, 1975
Use of the conditioning number k(F) = ∥ F ∥ • ∥ F−1 ∥ where F is a symmetric matrix related to the controllability (observability) matrix is suggested as basis for index of controllability (observability). This index has advantages of being independent of scaling of state variables and being a continuous function of parameters of process.
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Condition number

2001
Saul I. Gass, Carl M. Harris
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Condition Numbers

2000
Albrecht Böttcher, Sergei M. Grudsky
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Condition number

2011
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