6 papers · 1 filter
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…
Estimation of spectral gaps for sparse symmetric matrices
Michele Benzi, Michele Rinelli, Igor Simunec
In this paper we propose and analyze an algorithm for identifying spectral gaps of a real symmetric matrix by simultaneously approximating the traces of spectral projectors ass…
Analysis of stochastic probing methods for estimating the trace of functions of sparse symmetric matrices
Andreas Frommer, Michele Rinelli, Marcel Schweitzer
We consider the problem of estimating the trace of a matrix function . In certain situations, in particular if cannot be well approximated by a low-rank matrix, combin…
Refined decay bounds on the entries of spectral projectors associated with sparse Hermitian matrices
Michele Benzi, Michele Rinelli
Spectral projectors of Hermitian matrices play a key role in many applications, and especially in electronic structure computations. Linear scaling methods for gapped systems are b…