 
Summary: Numer. Math. 75: 267292 (1997)
Numerische
Mathematik
@ SpringerVerlag1997
On multisplitting methods for band matrices
Götz AlefeldI,Ingrid LenhardtI, Günter Mayer
I Institut für Angewandte Mathematik, Universität Karlsruhe, D76128 Karlsruhe, Germany
2 Fachbereich Mathematik, Universität Rostock, D18051 Rostock, Germany
Received July 18, 1994/ Revised version received November 20, 1995
Dedicated to J.W. Schmidt, Dresden, on the occasion of his 65th birthday
Summary. We present new theoretical results on two dasses of multisplitting
methods for solving linear systems iteratively. These dasses are based on over
lapping blocks of the underlying coefficient matrix A which is assumed to be
a band matrix. We show that under suitable conditions the spectral radius p(H)
of the iteration matrix H does not depend on the weights of the method even
if these weights are allowed to be negative. For a certain dass of splittings we
prove an optimality result for p(H) with respect to the weights provided that Ais
an Mmatrix. This result is based on the fact that the multisplitting method can
be represented by a single splittingA =M  N which in our situation surprisingly
turns out to be a regular splitting. Furthermore we show by numerical examples
