Results 241 to 250 of about 3,873,104 (284)

Condition number of Drazin inverse and their condition numbers of singular linear systems

Applied Mathematics and Computation, 2003
Various condition numbers are given for the Drazin inverse of a singular square matrix and for singular linear systems.
Wei, Yimin, Wang, Guanglin, Wang, Dingkun   +2 more
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Condition Number Estimation for Sparse Matrices

SIAM Journal on Scientific and Statistical Computing, 1981
The LINPACK package of linear equation solving software provides a reliable and inexpensive algorithm for estimating the condition number of a dense matrix. The direct generalization to banded or sparse matrices is reliable, but not necessarily inexpensive.
Grimes, Roger G., Lewis, John G.
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Smoothed analysis of some condition numbers

Numerical Linear Algebra with Applications, 2006
The authors in the paper first present a smoothed analysis of the condition number of \(A\) (in terms of its Moore-Penrose inversion \(A^{\dagger }\)) given as \(\kappa _{\dagger }(A) = \| A \| _2 \| A^{\dagger } \| _2\). They assume that a rectangular matrix \(A\) is Gaussian centered at \(M\) (i.e.\ its entries are independent normal variables with ...
Cucker, F., Diao, H., Wei, Y.
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Condition numbers for various FEM matrices

IEEE Antennas and Propagation Society International Symposium. 1999 Digest. Held in conjunction with: USNC/URSI National Radio Science Meeting (Cat. No.99CH37010), 1999
Summary: A detailed study is presented that examines the inter-relationships between condition numbers of finite element method (FEM) matrices based on various interpolatory and hierarchical tangential vector finite elements (TVFEs). The validity of the generally accepted postulate that interpolatory higher order TVFEs lead to better conditioned ...
Andersen, L. S., Volakis, J. L.
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Condition numbers and D-efficiency

Statistics & Probability Letters, 2004
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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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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