Fast and backward stable computation of roots of polynomials
A stable algorithm to compute the roots of polynomials is presented. The roots are found by
computing the eigenvalues of the associated companion matrix by Francis's implicitly shifted …
computing the eigenvalues of the associated companion matrix by Francis's implicitly shifted …
[图书][B] Core-chasing algorithms for the eigenvalue problem
Core-Chasing Algorithms for the Eigenvalue Problem : Back Matter Page 1 Bibliography [1] GS
Ammar, WB Gragg, and L. Reichel. On the eigenproblem for orthogonal matrices. In Proceedings …
Ammar, WB Gragg, and L. Reichel. On the eigenproblem for orthogonal matrices. In Proceedings …
Fast and backward stable computation of roots of polynomials, Part II: Backward error analysis; companion matrix and companion pencil
This work is a continuation of work by JL Aurentz, T. Mach, R. Vandebril, and DS Watkins, J.
Matrix Anal. Appl., 36 (2015), pp. 942--973. In that paper we introduced a companion QR …
Matrix Anal. Appl., 36 (2015), pp. 942--973. In that paper we introduced a companion QR …
Fast and backward stable computation of eigenvalues and eigenvectors of matrix polynomials
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 …
adequate linearizations and good scaling techniques for computing their eigenvalues and …
[PDF][PDF] Computing approximate (block) rational Krylov subspaces without explicit inversion with extensions to symmetric matrices
It has been shown that approximate extended Krylov subspaces can be computed, under
certain assumptions, without any explicit inversion or system solves. Instead, the vectors …
certain assumptions, without any explicit inversion or system solves. Instead, the vectors …
[PDF][PDF] Fast and stable unitary QR algorithm
A fast Fortran implementation of a variant of Gragg's unitary Hessenberg QR algorithm is
presented. It is proved, moreover, that all QR-and QZ-like algorithms for the unitary …
presented. It is proved, moreover, that all QR-and QZ-like algorithms for the unitary …
Fast QR iterations for unitary plus low rank matrices
R Bevilacqua, GM Del Corso, L Gemignani - Numerische Mathematik, 2020 - Springer
Some fast algorithms for computing the eigenvalues of a (block) companion matrix have
recently appeared in the literature. In this paper we generalize the approach to encompass …
recently appeared in the literature. In this paper we generalize the approach to encompass …
[HTML][HTML] An implicit filter for rational Krylov using core transformations
The rational Krylov method is a powerful tool for computing a selected subset of eigenvalues
in large-scale eigenvalue problems. In this paper we study a method to implicitly apply a …
in large-scale eigenvalue problems. In this paper we study a method to implicitly apply a …
[PDF][PDF] Roots of polynomials: on twisted QR methods for companion matrices and pencils
Two generalizations of the companion QR algorithm by JL Aurentz, T. Mach, R. Vandebril,
and DS Watkins, SIAM Journal on Matrix Analysis and Applications, 36 (3): 942–973, 2015 …
and DS Watkins, SIAM Journal on Matrix Analysis and Applications, 36 (3): 942–973, 2015 …
An extended Hamiltonian QR algorithm
M Ferranti, B Iannazzo, T Mach, R Vandebril - Calcolo, 2017 - Springer
An extended QR algorithm specifically tailored for Hamiltonian matrices is presented. The
algorithm generalizes the customary Hamiltonian QR algorithm with additional freedom in …
algorithm generalizes the customary Hamiltonian QR algorithm with additional freedom in …