Results 101 to 110 of about 98,636 (202)

Approximation of eigenvalues of some unbounded self-adjoint discrete Jacobi matrices by eigenvalues of finite submatrices [PDF]

Opuscula Mathematica, 2007
We investigate the problem of approximation of eigenvalues of some self-adjoint operator in the Hilbert space \(l^2(\mathbb{N})\) by eigenvalues of suitably chosen principal finite submatrices of an infinite Jacobi matrix that defines the operator ...
Maria Malejki
doaj  

The Spectrum of a Periodic Complex Jacobi Matrix Revisited

Journal of Approximation Theory, 2000
Let \(G\) be a complex periodic Jacobi matrix of period \(k\), i.e. \[ G=\begin{pmatrix} b^{(0)}&a^{(1)}&0&\cdots\\ a^{(1)}&b^{(1)}&a^{(2)}&\cdots\\ 0&a^{(2)}&b^{(2)}&\cdots\\ \vdots&\vdots&\vdots&\ddots\end{pmatrix}, \] where \(a^{(n)}=a^{(j)}\), \(b^{(n)}=b^{(j)}\) for \(n\equiv j\pmod k\). This matrix defines a bounded linear operator on \(\ell^2\).
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Combined Matrix of a Tridiagonal Toeplitz Matrix

Axioms
In this work, combined matrices of tridiagonal Toeplitz matrices are studied. The combined matrix is known as the Relative Gain Array in control theory.
Begoña Cantó, Rafael Cantó, Ana Maria Urbano   +2 more
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Moments of the free Jacobi process: A matrix approach

Canadian Mathematical Bulletin
AbstractWe compute the large size limit of the moment formula derived in [14] for the Hermitian Jacobi process at fixed time. Our computations rely on the polynomial division algorithm which allows to obtain cancellations similar to those obtained in [3, Lemma 3].
Nizar Demni, Tarek Hamdi
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Some Algorithms for Solving Third-Order Boundary Value Problems Using Novel Operational Matrices of Generalized Jacobi Polynomials

Abstract and Applied Analysis, 2015
The main aim of this research article is to develop two new algorithms for handling linear and nonlinear third-order boundary value problems. For this purpose, a novel operational matrix of derivatives of certain nonsymmetric generalized Jacobi ...
W. M. Abd-Elhameed
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A class of matrix-valued polynomials generalizing Jacobi polynomials

Journal of Approximation Theory, 2009
A hierarchy of matrix-valued polynomials which generalize the Jacobi polynomials is found. Defined by a Rodrigues formula, they are also products of a sequence of differential operators. Each class of polynomials is complete, satisfies a two-step recurrence relation, integral inter-relations, and quasi-orthogonality relations.
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A study on almost matrix summability of Fourier-Jacobi series [PDF]

Surveys in Mathematics and its Applications, 2011
In this paper, a quite new theorem on almost summability of Fourier-Jacobi series has been established. Our theorem extends and generalizes all previously known results of this line of work.
Hare Krishna Nigam , Ajay Sharma
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The Smith normal form of a specialized Jacobi–Trudi matrix

European Journal of Combinatorics, 2017
5 pages, 2 ...
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The Matrix Representations of Centroids for Low-Dimensional Mock-Lie Algebras

Journal of Mathematics
Mock-Lie algebras, a unique class of commutative algebras that satisfy the Jacobi identity, are gaining attention for their potential applications in various mathematical contexts.
Yue Zhu, Keli Zheng
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On the optimal selection of the relaxation constant in the JOR method

Journal of Numerical Analysis and Approximation Theory, 2003
In this paper we suggest a method for the quasi-optimal selection of the relaxation constant in the Jacobi overrelaxation (JOR) method. It is assumed that the eigenvalues of the coefficient matrix belong to a rectangular region. Our estimates may lead to
Slobodan Lakić, Ferenc Szidarovszky
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