Tridiagonal test matrices for eigenvalue computations: two-parameter extensions of the Clement matrix

DOI10.1016/j.cam.2016.10.019zbMath1354.65075arXiv1612.07619OpenAlexW2547640630MaRDI QIDQ345959

Joris Van der Jeugt, Roy Oste

Publication date: 2 December 2016

Published in: Journal of Computational and Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1612.07619

zbMATH Keywords

tridiagonal matrixnumerical resultClement matrixeigenvalue computationexact eigenvaluesinteger entriesSylvester-Kac matrix

Mathematics Subject Classification ID

Computational methods for sparse matrices (65F50) Numerical computation of eigenvalues and eigenvectors of matrices (65F15) Eigenvalues, singular values, and eigenvectors (15A18) Matrices of integers (15B36)

Related Items (12)

Schrödinger's tridiagonal matrix ⋮ ON GAUSSIAN FIBONACCI-SYLVESTER-KAC MATRIX ⋮ FERMAT-SYLVESTER-KAC MATRIX ⋮ Efficient computation of tridiagonal matrices largest eigenvalue ⋮ Characteristic polynomial, determinant and inverse of a Fibonacci-Sylvester-Kac matrix ⋮ A short note on the determinant of a Sylvester-Kac type matrix ⋮ Unnamed Item ⋮ Elliptic Kac-Sylvester matrix from difference Lamé equation ⋮ $q$-Deformation of the Kac-Sylvester tridiagonal matrix ⋮ Spectrum and eigenvectors for a class of tridiagonal matrices ⋮ Persymmetric Jacobi matrices with square-integer eigenvalues and dispersionless mass-spring chains ⋮ A new type of Sylvester–Kac matrix and its spectrum

Uses Software

• testmatrix

Cites Work

• Krawtchouk polynomials, the Lie algebra \(\mathfrak{sl}_2\), and Leonard pairs
• Homotopy method for the eigenvalues of symmetric tridiagonal matrices
• The eigenvalues of a tridiagonal matrix in biogeography
• From the Ehrenfest model to time-fractional stochastic processes
• Another look at a matrix of Mark Kac
• An explicit formula for singular values of the Sylvester-Kac matrix
• Doubling (dual) Hahn polynomials: classification and applications
• A note on the eigenvalues of a special class of matrices
• Hyman's method revisited
• The Sylvester-Kac matrix space
• A finite oscillator model with equidistant position spectrum based on an extension of ${\mathfrak{su}}(2)$
• Finite oscillator models: the Hahn oscillator
• Hypergeometric Orthogonal Polynomials and Their q-Analogues
• A Class of Triple-Diagonal Matrices for Test Purposes
• Random Walk and the Theory of Brownian Motion
• A generalized eigenvalue algorithm for tridiagonal matrix pencils based on a nonautonomous discrete integrable system
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