N. J. Higham, F. Tisseur, Nicholas J. Higham
De nitions and characterizations of pseudospectra are given for rectangular matrix polynomials expressed in homogeneous form: P (; ) = ( d A d + d 1 A d 1 +
Implicit Gamma Theorems (I): (2007)
J. P. Dedieu, M. Shub, F. Tisseur, Jean-pierre Dedieu, Myong-hi Kim, ...
Hilbert
Bounds for Eigenvalues of Matrix Polynomials (2003)
N. J. Higham, F. Tisseur, Nicholas J. Higham
Upper and lower bounds are derived for the absolute values of the eigenvalues of a matrix polynomial (or -matrix). The bounds are based on norms of the coecient matrices and involve the inverses of...
Perturbation theory for homogeneous polynomial eigenvalue problems (2001)
F. Tisseur, Jean-pierre Dedieu, Francoise Tisseur
We consider polynomial eigenvalue problems P (A; ff; fi)x = 0 in which the matrix polynomial is homogeneous in the eigenvalue (ff; fi) 2 C 2. In this framework infinite eigenvalues are on the same...
A survey of the quadratic eigenvalue problem (2001)
F. Tisseur, K. Meerbergen, Francoise Tisseur
y Abstract. We survey the quadratic eigenvalue problem, treating its many applications, its mathematical properties, and a variety of numerical solution techniques. Emphasis is given to exploiting...
We present a chart of structured backward errors for approximate eigenpairs of singly and doubly structured eigenvalue problems. We aim to give, wherever possible, formulae that are inexpensive to...
Stability of Structured Hamiltonian Eigensolvers (2000)
. Various applications give rise to eigenvalue problems for which the matrices are Hamiltonian or skew-Hamiltonian and also symmetric or skew-symmetric. We define structured backward errors that are...
F Tisseur, J Dongarra, Mims Eprint, Françoise Tisseur, Jack Dongarra
Abstract. We present a new parallel implementation of a divide and conquer algorithm for computing the spectral decomposition of a symmetric tridiagonal matrix on distributed memory architectures....