A generalized eigenvalue algorithm for tridiagonal matrix pencils based on a nonautonomous discrete integrable system
Copyright policy )A generalized eigenvalue algorithm for tridiagonal matrix pencils based on a nonautonomous discrete integrable system
A generalized eigenvalue algorithm for tridiagonal matrix pencils is presented. The algorithm appears as the time evolution equation of a nonautonomous discrete integrable system associated with a polynomial sequence which has some orthogonality on the support set of the zeros of the characteristic polynomial for a tridiagonal matrix pencil. The convergence of the algorithm is discussed by using the solution to the initial value problem for the corresponding discrete integrable system.
24 pages, 2 figures, 3 tables
Numerical computation of eigenvalues and eigenvectors of matrices, Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests, generalized eigenvalue problem, convergence, Nonlinear Sciences - Exactly Solvable and Integrable Systems, 37K10, 37K40, 42C05, 65F15, nonautonomous discrete integrable system, FOS: Physical sciences, Numerical Analysis (math.NA), Computational methods for sparse matrices, tridiagonal matrix pencils, FOS: Mathematics, Mathematics - Numerical Analysis, Exactly Solvable and Integrable Systems (nlin.SI), Matrix pencils, initial value problem, orthogonal polynomials, dqds algorithm, \(\text{R}_{\operatorname{II}}\)-chain
Numerical computation of eigenvalues and eigenvectors of matrices, Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests, generalized eigenvalue problem, convergence, Nonlinear Sciences - Exactly Solvable and Integrable Systems, 37K10, 37K40, 42C05, 65F15, nonautonomous discrete integrable system, FOS: Physical sciences, Numerical Analysis (math.NA), Computational methods for sparse matrices, tridiagonal matrix pencils, FOS: Mathematics, Mathematics - Numerical Analysis, Exactly Solvable and Integrable Systems (nlin.SI), Matrix pencils, initial value problem, orthogonal polynomials, dqds algorithm, \(\text{R}_{\operatorname{II}}\)-chain
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