Re: How to solver the following system efficiently?

tangtang wrote:
Hi all,

I have the following blocked complex matrix:

m n k
m [ A B C ] [ x1 ] [ b1 ]
n [ D E F ] [ x2 ] = [ b2 ]
k [ G H P ] [ x3 ] [ b3 ]

Where A is a symmetric positive definite matrix with the size m*m; E is the matrix with the size n*n;
P is the matrix with the size k*k.

Usually m >> k >> n and the condition of other matrices are very bad. Furthermore, there could be very large or small value in the matrices except A.

Suppose I have very efficient solver to solve the matrix A, is there any efficient method to solve the whole system?


You have several options - just treat the matrices as if they were numbers
- except when you need division, do a left multiplication by the inverse
of the corresponding matrix.

I'd try
- Block Jacobi iteration ( if it converges )
- Block Gauss-Seidel iteration ( if it converges )
- Block Gaussian elimination leading to a Schur complement.



--
Helmut Jarausch

Lehrstuhl fuer Numerische Mathematik
RWTH - Aachen University
D 52056 Aachen, Germany
.