scholarly journals Correction to: On the condition number of Vandermonde matrices with pairs of nearly-colliding nodes

2020 ◽  
Author(s):  
Stefan Kunis ◽  
Dominik Nagel
Keyword(s):  
Condition Number ◽  
Vandermonde Matrices

Lower bounds for the condition number of Vandermonde matrices

1987 ◽  
Vol 52 (3) ◽  
pp. 241-250 ◽  
Author(s):  
Walter Gautschi ◽  
Gabriele Inglese
Keyword(s):  
Lower Bounds ◽  
Condition Number ◽  
Vandermonde Matrices

scholarly journals On the condition number of Vandermonde matrices with pairs of nearly-colliding nodes

2020 ◽  
Author(s):  
Stefan Kunis ◽  
Dominik Nagel
Keyword(s):  
Unit Circle ◽  
Lower Bounds ◽  
Condition Number ◽  
Growth Rates ◽  
Separation Distance ◽  
Upper And Lower Bounds ◽  
Spectral Condition ◽  
Sharp Constants ◽  
Vandermonde Matrices

Abstract We prove upper and lower bounds for the spectral condition number of rectangular Vandermonde matrices with nodes on the complex unit circle. The nodes are “off the grid,” pairs of nodes nearly collide, and the studied condition number grows linearly with the inverse separation distance. Such growth rates are known in greater generality if all nodes collide or for groups of colliding nodes. For pairs of nodes, we provide reasonable sharp constants that are independent of the number of nodes as long as non-colliding nodes are well-separated.

scholarly journals Some Characterizations of the Distribution of the Condition Number of a Complex Gaussian Matrix

2020 ◽  
Vol 8 (1) ◽  
pp. 22-35
Author(s):  
M. Shakil ◽  
M. Ahsanullah
Keyword(s):  
Order Statistics ◽  
Condition Number ◽  
Record Values ◽  
Distributional Properties ◽  
Upper Record Values ◽  
Upper Record

AbstractThe objective of this paper is to characterize the distribution of the condition number of a complex Gaussian matrix. Several new distributional properties of the distribution of the condition number of a complex Gaussian matrix are given. Based on such distributional properties, some characterizations of the distribution are given by truncated moment, order statistics and upper record values.

Schur complement spectral bounds for large hybrid FETI-DP clusters and huge three-dimensional scalar problems

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Zdeněk Dostál ◽  
Tomáš Brzobohatý ◽  
Oldřich Vlach
Keyword(s):  
Condition Number ◽  
Three Dimensional ◽  
Schur Complement ◽  
Decomposition Methods ◽  
Stiffness Matrices ◽  
Spectral Bounds ◽  
Schur Complements ◽  
Linear Problems ◽  
Primal Method ◽  
Large Clusters

Abstract Bounds on the spectrum of Schur complements of subdomain stiffness matrices with respect to the interior variables are key ingredients of the convergence analysis of FETI (finite element tearing and interconnecting) based domain decomposition methods. Here we give bounds on the regular condition number of Schur complements of “floating” clusters arising from the discretization of 3D Laplacian on a cube decomposed into cube subdomains. The results show that the condition number of the cluster defined on a fixed domain decomposed into m × m × m cube subdomains connected by face and optionally edge averages increases proportionally to m. The estimates support scalability of unpreconditioned H-FETI-DP (hybrid FETI dual-primal) method. Though the research is most important for the solution of variational inequalities, the results of numerical experiments indicate that unpreconditioned H-FETI-DP with large clusters can be useful also for the solution of huge linear problems.

scholarly journals The spectral condition number plot for regularization parameter evaluation

2019 ◽  
Vol 35 (2) ◽  
pp. 629-646 ◽  
Author(s):  
Carel F. W. Peeters ◽  
Mark A. van de Wiel ◽  
Wessel N. van Wieringen
Keyword(s):  
Condition Number ◽  
Regularization Parameter ◽  
Spectral Condition ◽  
Parameter Evaluation
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