74 citations · 122 across the 32 of their papers we have counts for
7 papers · 2 filters
Fast Hessenberg reduction of some rank structured matrices
Luca Gemignani, Leonardo Robol
We develop two fast algorithms for Hessenberg reduction of a structured matrix where is a real or unitary diagonal matrix and $U, V \in\mathbb{C}^{n…
Fast and backward stable computation of the eigenvalues and eigenvectors of matrix polynomials
Jared Aurentz, Thomas Mach, Leonardo Robol +2
In the last decade matrix polynomials have been investigated with the primary focus on adequate linearizations and good scaling techniques for computing their eigenvalues and eigen…
Fast and backward stable computation of roots of polynomials, Part II: backward error analysis; companion matrix and companion pencil
Jared L. Aurentz, Thomas Mach, Leonardo Robol +2
This work is a continuation of "Fast and backward stable computation of roots of polynomials" by J.L. Aurentz, T. Mach, R. Vandebril, and D.S. Watkins, SIAM Journal on Matrix Analy…
On the decay of the off-diagonal singular values in cyclic reduction
Dario Andrea Bini, Stefano Massei, Leonardo Robol
It was recently observed that the singular values of the off-diagonal blocks of the matrix sequences generated by the Cyclic Reduction algorithm decay exponentially. This property…
Decay bounds for the numerical quasiseparable preservation in matrix functions
Stefano Massei, Leonardo Robol
Given matrices and such that , where is a holomorphic function, we analyze the relation between the singular values of the off-diagonal submatrices of an…
A framework for structured linearizations of matrix polynomials in various bases
Leonardo Robol, Raf Vandebril, Paul Van Dooren
We present a framework for the construction of linearizations for scalar and matrix polynomials based on dual bases which, in the case of orthogonal polynomials, can be described b…
Efficient cyclic reduction for QBDs with rank structured blocks
Dario A. Bini, Stefano Massei, Leonardo Robol
We provide effective algorithms for solving block tridiagonal block Toeplitz systems with quasiseparable blocks, as well as quadratic matrix equations with …