[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 …
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
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 …
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 …
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 …
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 …
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 …
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 …
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 …
recurrence relations connecting two sets of Hahn, dual Hahn or Racah polynomials of the …