The Stability Analysis of Linear Systems with Cauchy-Polynomial-Vandermonde Matrices

被引：0
|
作者：
Rehman, Mutti-Ur [1 ]
Alzabut, Jehad [2 ,3 ]
Fatima, Nahid [2 ]
Rasulov, Tulkin H. [1 ]
机构：
[1] Bukhara State Univ, Dept Math Anal, Bukhara 200100, Uzbekistan
[2] Prince Sultan Univ, Dept Math & Sci, Riyadh 11586, Saudi Arabia
[3] OSTIM Tech Univ, Dept Ind Engn, Turkiye, TR-06374 Ankara, Turkiye
来源：
AXIOMS | 2023年 / 12卷 / 09期
关键词：
mu-values; singular values; eigenvalues; structured matrices; DISPLACEMENT-STRUCTURE APPROACH; CHEBYSHEV-VANDERMONDE; SINGULAR-VALUES; ACCURATE COMPUTATIONS; ALGORITHM; APPROXIMATION; DECOMPOSITION; FACTORIZATION; EIGENVALUES; SVDS;
D O I：
10.3390/axioms12090831
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
The numerical approximation of both eigenvalues and singular values corresponding to a class of totally positive Bernstein-Vandermonde matrices, Bernstein-Bezoutian structured matrices, Cauchy-polynomial-Vandermonde structured matrices, and quasi-rational Bernstein-Vandermonde structured matrices are well studied and investigated in the literature. We aim to present some new results for the numerical approximation of the largest singular values corresponding to Bernstein-Vandermonde, Bernstein-Bezoutian, Cauchy-polynomial-Vandermonde and quasi-rational Bernstein-Vandermonde structured matrices. The numerical approximation for the reciprocal of the largest singular values returns the structured singular values. The new results for the numerical approximation of bounds from below for structured singular values are accomplished by computing the largest singular values of totally positive Bernstein-Vandermonde structured matrices, Bernstein-Bezoutian structured matrices, Cauchy-polynomial-Vandermonde structured matrices, and quasi-rational Bernstein-Vandermonde structured matrices. Furthermore, we present the spectral properties of totally positive Bernstein-Vandermonde structured matrices, Bernstein-Bezoutian structured matrices, Cauchy-polynomial-Vandermonde structured matrices, and structured quasi-rational Bernstein-Vandermonde matrices by computing the eigenvalues, singular values, structured singular values and its lower and upper bounds and condition numbers.
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页数：21
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