12 papers
Fast computation of eigenvalues of periodic CMV matrices
Thomas Mach, Michele Rinelli, Raf Vandebril +1
Periodic CMV matrices are unitary matrices that can be specified by data. Their eigenvalues can be computed by standard methods, storing them as conventional matrices (using…
Block Krylov subspaces and orthogonal matrix polynomials: a structural correspondence with applications to unitary matrices
Michele Rinelli, Raf Vandebril
We study the connection between block Krylov subspaces and matrix orthogonal functions. Under a no-deflation assumption, we show that polynomial block Krylov subspaces are isometri…
Krylov and core transformation algorithms for an inverse eigenvalue problem to compute recurrences of multiple orthogonal polynomials
Amin Faghih, Michele Rinelli, Marc Van Barel +2
In this paper, we develop algorithms for computing the recurrence coefficients corresponding to multiple orthogonal polynomials on the step-line. We reformulate the problem as an i…
ParaSLRF: A High Performance Rational Filter Method for Solving Large Scale Eigenvalue Problems
Biyi Wang, Karl Meerbergen, Raf Vandebril +2
In \emph{Wang et al., A Shifted Laplace Rational Filter for Large-Scale Eigenvalue Problems}, the SLRF method was proposed to compute all eigenvalues of a symmetric definite genera…
The RQR algorithm
Daan Camps, Thomas Mach, Raf Vandebril +1
Pole-swapping algorithms, generalizations of bulge-chasing algorithms, have been shown to be a viable alternative to the bulge-chasing QZ algorithm for solving the generalized eige…
Manifold-valued function approximation from multiple tangent spaces
Hang Wang, Raf Vandebril, Joeri Van der Veken +1
Approximating a manifold-valued function from samples of input-output pairs consists of modeling the relationship between an input from a vector space and an output on a Riemannian…