Optimal multi-input–multi-output relay transform matrix with a bounded condition number

2014 ◽  
Vol 8 (15) ◽  
pp. 2713-2719
Author(s):  
Mohammad Hassan Shariat ◽  
Mehrzad Biguesh ◽  
Saeed Gazor
Keyword(s):  
Condition Number ◽  
Transform Matrix

Effect of the Condition Number of the Inverse Fourier Transform Matrix on the Solution Behavior of the Time Spectral Equation System

2020 ◽  
Author(s):  
Sen Zhang ◽  
Dingxi Wang ◽  
Yi Li ◽  
Hangkong Wu ◽  
Xiuquan Huang
Keyword(s):  
Fourier Transform ◽  
Stability Analysis ◽  
Condition Number ◽  
Inverse Fourier Transform ◽  
Real Life ◽  
Equation System ◽  
Time Instant ◽  
Transform Matrix ◽  
Spectral Equation ◽  
The Impact

Abstract The time spectral method is a very popular reduced order frequency method for analyzing unsteady flow due to its advantage of being easily extended from an existing steady flow solver. Condition number of the inverse Fourier transform matrix used in the method can affect the solution convergence and stability of the time spectral equation system. This paper aims at evaluating the effect of the condition number of the inverse Fourier transform matrix on the solution stability and convergence of the time spectral method from two aspects. The first aspect is to assess the impact of condition number using a matrix stability analysis based upon the time spectral form of the scalar advection equation. The relationship between the maximum allowable Courant number and the condition number will be derived. Different time instant groups which lead to the same condition number are also considered. Three numerical discretization schemes are provided for the stability analysis. The second aspect is to assess the impact of condition number for real life applications. Two case studies will be provided: one is a flutter case, NASA rotor 67, and the other is a blade row interaction case, NASA stage 35. A series of numerical analyses will be performed for each case using different time instant groups corresponding to different condition numbers. The conclusion drawn from the two real life case studies will corroborate the relationship derived from the matrix stability analysis.

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

scholarly journals Improving the condition number of a simple eigenvalue by a rank one matrix

2016 ◽  
Vol 58 ◽  
pp. 7-12
Author(s):  
Rafael Bru ◽  
Rafael Cantó ◽  
Ana M. Urbano
Keyword(s):  
Condition Number ◽  
Simple Eigenvalue ◽  
Rank One

Condition number related to the outer inverse of a complex matrix

2009 ◽  
Vol 215 (8) ◽  
pp. 2826-2834 ◽  
Author(s):  
Dijana Mosić ◽  
Dragan S. Djordjević
Keyword(s):  
Condition Number ◽  
Complex Matrix ◽  
Outer Inverse
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