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 Abdulhafid Elfaghi September 15, 2007 13:55

Block-Block tridiagonal matrix inverse

I am trying to solve systems of linear equations Au=b where the coefficient matrix A possesses a block tridiagonal structure with each of the block matrices is block tridiagonal as well. Anyone who can help me to solve this system of linear equations. is there any available algorithm for the inversion of block-block tridiagonal matrix?

 otd September 15, 2007 18:14

Re: Block-Block tridiagonal matrix inverse

Don't know if there's a special algorithm for the inner set of blocks, but the 'standard' block triagonal algorithm should work.

Are you sure you need the inverse? Factoring the matrix into upper and lower triangular parts is much more efficient if you really just need the vector "u".

Beyond this answer, some help from a linear algebra expert is in order.

Good luck!

 Dominic September 15, 2007 23:26

Re: Block-Block tridiagonal matrix inverse

Hi,

The discretization of a Poisson Equation results in these Block-Block Tridiagonal Matrices. There are lots of open source packages which you can use to solve these type of equations. LAPACK, SuperLU, PETSc.. Actually you will not need to construct the inverse to solve these type of problems.. Direct methods such as LU and iterative methods such as GMRES/Conjugate Gradient should solve your problem.

-Dominic

 sandy September 16, 2007 02:55

Re: Block-Block tridiagonal matrix inverse