Circulant-like Preconditioners for
Circulant-like Preconditioners for
Nonsymmetric Block Toeplitz Linear Systems
Daniele BERTACCINI
Dipartimento di Matematica
Università di Roma ``La Sapienza"
Italy
Email: bertaccini@mat.uniroma1.it
In this talk we discuss the conditioning and
asymptotical spectral properties of some circulant and
circulant-like approximations used in block preconditioners for
nonsymmetric block Toeplitz linear systems whose matrices can be
written as
where A and B are Toeplitz(-like) matrices and R is large
and sparse. These linear systems arise in finite difference and
finite elements discretization of, e.g., time-dependent partial
differential equations. In particular, we will focus on linear
systems arising in the finite difference discretization by using
linear multistep formulas in boundary value form and we will
consider preconditioners which can be represented in matrix form
as P = c(A)ÄI-c(B)ÄR, where c(A) and c(B) are
circulant-like approximations of A and B, respectively.
Some comments on the convergence behavior of GMRES,
BiCG-like and conjugate gradient for the normal equations using
various possible circulant-like approximations c(A) and c(B) will
be proposed as well.
File translated from TEX by TTH, version 1.94.
On 10 Apr 2002, 22:51.