167 1995 Sverker Holmgren and Kurt Otto sverker@tdb.uu.se A framework for polynomial preconditioners based on fast transforms I: Theory
Abstract
Optimal and superoptimal approximations of a square matrix
by polynomials in a normal basis matrix are considered.
If the unitary transform associated with the eigenvectors of
the basis matrix is computable using a fast algorithm, the approximations
may be utilized for constructing preconditioners. Theorems describing how
the parameters of the approximations could be efficiently computed
are given, and for special cases earlier results by other authors
are recovered. Also, optimal and superoptimal approximations for
block matrices are determined, and the same type of theorems as for
the point case are proved.