Results 1 to 10 of about 484,399 (236)
Journal of Computational and Applied Mathematics, 2001 This paper surveys and extends recent work on the connections between formal orthogonal polynomials, complex Jacobi continued fractions (\(J\)-fractions) and spectral properties of the underlying infinite complex symmetric tridiagonal (Jacobi) matrix. Special emphasis is given to unbounded recurrence coefficients.
Beckermann, Bernhard
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A reliable computational approach for fractional isothermal chemical model
Alexandria Engineering JournalThis article analyzes and computes numerical solutions for the fractional isothermal chemical (FIC) model. This work suggested a Jacobi collocation method (JCM) to examine the FIC model.
Devendra Kumar +2 more
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Construction of Fractional Pseudospectral Differentiation Matrices with Applications
AxiomsDifferentiation matrices are an important tool in the implementation of the spectral collocation method to solve various types of problems involving differential operators.
Wenbin Li, Hongjun Ma, Tinggang Zhao
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The Szegő condition for Coulomb Jacobi matrices
Journal of Approximation Theory, 2003 A Jacobi matrix with $a_n\to 1$, $b_n\to 0$ and spectral measure $ν'(x)dx + dν_{sing}(x)$ satisfies the Szeg\H o condition if $\int_{0}^π\ln \bigl[ ν'(2\cosθ) \bigr] dθ$ is finite. We prove that if $a_n = 1 + \frac α{n} + O(n^{-1-\eps})$ and $b_n = \frac β{n} + O(n^{-1-\eps})$ with $2α\ge |β|$ and $\eps>0$, then the corresponding matrix is Szeg\H o.
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The Stenger conjectures and the A-stability of collocation Runge-Kutta methods
Journal of Inequalities and Applications, 2023 Stenger conjectures are claims about the location of the eigenvalues of matrices whose elements are certain integrals involving basic Lagrange interpolating polynomials supported on the zeros of orthogonal polynomials. In this paper, we show the validity
Rachid Ait-Haddou, Hoda Alselami
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Inverse Spectral Problems for Tridiagonal N by N Complex Hamiltonians
Symmetry, Integrability and Geometry: Methods and Applications, 2009 In this paper, the concept of generalized spectral function is introduced for finite-order tridiagonal symmetric matrices (Jacobi matrices) with complex entries.
Gusein Sh. Guseinov
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A first-order spectral phase transition in a class of periodically modulated Hermitian Jacobi matrices [PDF]
Opuscula Mathematica, 2008 We consider self-adjoint unbounded Jacobi matrices with diagonal \(q_n = b_{n}n\) and off-diagonal entries \(\lambda_n = n\), where \(b_{n}\) is a \(2\)-periodical sequence of real numbers. The parameter space is decomposed into several separate regions,
Irina Pchelintseva
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On classical orthogonal polynomials and the Cholesky factorization of a class of Hankel matrices
Bulletin of Mathematical SciencesClassical moment functionals (Hermite, Laguerre, Jacobi, Bessel) can be characterized as those linear functionals whose moments satisfy a second-order linear recurrence relation.
Misael E. Marriaga +3 more
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Dynamic inverse problem for Jacobi matrices
Inverse Problems and Imaging, 2019 We consider the inverse dynamical problem for the dynamical system with discrete time associated with the semi-infinite Jacobi matrix. We solve the inverse problem for such a system and answer a question on the characterization of the inverse data. As a by-product we give a necessary and sufficient condition for the measure on the real line line to be ...
Mikhaylov, A. S., Mikhaylov, V. S.
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Finite Gap Jacobi Matrices: A Review
, 2013 Perhaps the most common theme in Fritz Gesztesy's broad opus is the study of problems with periodic or almost periodic finite gap differential and difference equations, especially those connected to integrable systems. The present paper reviews recent progress in the understanding of finite gap Jacobi matrices and their perturbations.
Christiansen, Jacob S. +2 more
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