Abstract
In this paper we describe an orthogonal similarity transformation for
transforming arbitrary symmetric matrices into a diagonal-plus-semiseparable
matrix, where we can freely choose the diagonal. Very recently an algorithm was
proposed for transforming arbitrary symmetric matrices into similar semiseparable
ones. This reduction is strongly connected to the reduction to tridiagonal form. The
class of semiseparable matrices can be considered as a subclass of the diagonalplus-
semiseparable matrices. Therefore we can interpret the proposed algorithm
here as an extension of the reduction to semiseparable form.
A numerical experiment is performed comparing thereby the accuracy of this
reduction algorithm with respect to the accuracy of the traditional reduction to tridiagonal
form, and the reduction to semiseparable form. The experiment indicates
that all three reduction algorithms are equally accurate. Moreover it is shown in the experiments that asymptotically all the three approaches have the same complexity, i.e. that they have the same factor preceding the nxnxn term in the computational
complexity. Finally we illustrate that special choices of the diagonal create a
specific convergence behavior.
Anno
2006
Autori IAC
Tipo pubblicazione
Altri Autori
Raf Vandebril; Ellen Van Camp; Marc Van Barel; Nicola Mastronardi
Editore
Springer
Rivista
Numerische Mathematik