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

R Oste, J Van der Jeugt - Journal of Computational and Applied …, 2017 - Elsevier
Abstract The Clement or Sylvester–Kac matrix is a tridiagonal matrix with zero diagonal and
simple integer entries. Its spectrum is known explicitly and consists of integers which makes …

A four parameter extension to the Clement matrix and its role in numerical software testing

A Alazemi, T Hopkins, E Kılıç - Journal of Computational and Applied …, 2024 - Elsevier
Abstract The Sylvester–Kac matrix (also known as the Clement matrix) and its
generalizations are of interest to researchers in diverse fields. A new parameterization of the …

Schrödinger's tridiagonal matrix

A Kovačec - Special Matrices, 2021 - degruyter.com
In the third part of his famous 1926 paper 'Quantisierung als Eigenwertproblem',
Schrödinger came across a certain parametrized family of tridiagonal matrices whose …

𝑞-Deformation of the Kac-Sylvester tridiagonal matrix

J van Diejen - Proceedings of the American Mathematical Society, 2021 - ams.org
Upon replacing integers by $ q $-integers, one arrives at a natural $ q $-deformation of a
remarkably ubiquitous tridiagonal integer matrix whose eigenvalues and eigenvectors were …

A finite oscillator model with equidistant position spectrum based on an extension of

R Oste, J Van der Jeugt - Journal of Physics A: Mathematical and …, 2016 - iopscience.iop.org
We consider an extension of the real Lie algebra ${\mathfrak {su}}(2) $ by introducing a
parity operator P and a parameter c. This extended algebra is isomorphic to the Bannai–Ito …

A finite quantum oscillator model related to special sets of Racah polynomials

R Oste, J Van der Jeugt - Physics of Atomic Nuclei, 2017 - Springer
Abstract In [R. Oste and J. Van der Jeugt, arXiv: 1507.01821 [math-ph]] we classified all pairs
of recurrence relations in which two (dual) Hahn polynomials with different parameters …

Linear differential operators with polynomial coefficients generating generalised Sylvester-Kac matrices

A Dyachenko, M Tyaglov - arXiv preprint arXiv:2104.01216, 2021 - arxiv.org
A method of generating differential operators is used to solve the spectral problem for a
generalisation of the Sylvester-Kac matrix. As a by-product, we find a linear differential …

Algebraic structures related to Racah doubles

R Oste, J Van der Jeugt - Lie Theory and Its Applications in Physics: Varna …, 2016 - Springer
Abstract In Oste and Van der Jeugt, SIGMA, 12 (2016),[13], we classified all pairs of
recurrence relations connecting two sets of Hahn, dual Hahn or Racah polynomials of the …