Michele Rinelli
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View article: Krylov and core transformation algorithms for an inverse eigenvalue problem to compute recurrences of multiple orthogonal polynomials
Krylov and core transformation algorithms for an inverse eigenvalue problem to compute recurrences of multiple orthogonal polynomials Open
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 inverse eigenvalue problem, which can be solved using numeri…
View article: Estimation of spectral gaps for sparse symmetric matrices
Estimation of spectral gaps for sparse symmetric matrices Open
In this paper we propose and analyze an algorithm for identifying spectral gaps of a real symmetric matrix $A$ by simultaneously approximating the traces of spectral projectors associated with multiple different spectral slices. Our method…
View article: Analysis of stochastic probing methods for estimating the trace of functions of sparse symmetric matrices
Analysis of stochastic probing methods for estimating the trace of functions of sparse symmetric matrices Open
We consider the problem of estimating the trace of a matrix function $f(A)$. In certain situations, in particular if $f(A)$ cannot be well approximated by a low-rank matrix, combining probing methods based on graph colorings with stochasti…
View article: Computation of the von Neumann entropy of large matrices via trace estimators and rational Krylov methods
Computation of the von Neumann entropy of large matrices via trace estimators and rational Krylov methods Open
We consider the problem of approximating the von Neumann entropy of a large, sparse, symmetric positive semidefinite matrix $A$, defined as $\operatorname{tr}(f(A))$ where $f(x)=-x\log x$. After establishing some useful properties of this …
View article: Refined decay bounds on the entries of spectral projectors associated with sparse Hermitian matrices
Refined decay bounds on the entries of spectral projectors associated with sparse Hermitian matrices Open
Spectral projectors of Hermitian matrices play a key role in many applications, such as electronic structure computations. Linear scaling methods for gapped systems are based on the fact that these special matrix functions are localized, w…
View article: Refined decay bounds on the entries of spectral projectors associated with sparse Hermitian matrices
Refined decay bounds on the entries of spectral projectors associated with sparse Hermitian matrices Open
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 based on the fact that these special matrix functions are lo…