scholarly journals Spectral theory of the G-symmetric tridiagonal matrices related to Stahl’s counterexample

2015 ◽  
Vol 191 ◽  
pp. 58-70
Author(s):  
Maxim Derevyagin
Keyword(s):  
Spectral Theory ◽  
Tridiagonal Matrices

Ninety years of k-tridiagonal matrices

2020 ◽  
Vol 57 (3) ◽  
pp. 298-311
Author(s):  
Carlos M. da Fonseca ◽  
Victor Kowalenko ◽  
László Losonczi
Keyword(s):  
Spectral Theory ◽  
Trigonometric Polynomials ◽  
Structured Matrices ◽  
Tridiagonal Matrices ◽  
Seminal Article

AbstractThis survey revisits Jenő Egerváry and Otto Szász’s article of 1928 on trigonometric polynomials and simple structured matrices focussing mainly on the latter topic. In particular, we concentrate on the spectral theory for the first type of the matrices introduced in the article, which are today referred to as k-tridiagonal matrices, and then discuss the explosion of interest in them over the last two decades, most of which could have benefitted from the seminal article, had it not been overlooked.

To the spectral theory of partially ordered sets

2018 ◽  
Vol 60 (3) ◽  
pp. 578-598
Author(s):  
Yu. L. Ershov ◽  
M. V. Schwidefsky
Keyword(s):  
Spectral Theory ◽  
Partially Ordered Sets ◽  
Ordered Sets ◽  
Partially Ordered

SPECTRAL THEORY OF 2-D PHOTONIC CRYSTALS: ANALYTICAL GROUNDS

2016 ◽  
Vol 75 (16) ◽  
pp. 1417-1433 ◽  
Author(s):  
Yurii Konstantinovich Sirenko ◽  
K. Yu. Sirenko ◽  
H. O. Sliusarenko ◽  
N. P. Yashina
Keyword(s):  
Photonic Crystals ◽  
Spectral Theory

scholarly journals Inversion of Tridiagonal Matrices Using the Dunford-Taylor’s Integral

Symmetry ◽  
2021 ◽  
Vol 13 (5) ◽  
pp. 870
Author(s):  
Diego Caratelli ◽  
Paolo Emilio Ricci
Keyword(s):  
Functional Analysis ◽  
Computer Algebra ◽  
Toeplitz Matrices ◽  
Test Cases ◽  
Recursive Procedure ◽  
Tridiagonal Matrices ◽  
Special Cases ◽  
The Matrix ◽  
Matrix Eigenvalues ◽  
Complex Valued

We show that using Dunford-Taylor’s integral, a classical tool of functional analysis, it is possible to derive an expression for the inverse of a general non-singular complex-valued tridiagonal matrix. The special cases of Jacobi’s symmetric and Toeplitz (in particular symmetric Toeplitz) matrices are included. The proposed method does not require the knowledge of the matrix eigenvalues and relies only on the relevant invariants which are determined, in a computationally effective way, by means of a dedicated recursive procedure. The considered technique has been validated through several test cases with the aid of the computer algebra program Mathematica©.

Sign in / Sign up

Export Citation Format

Share Document