Iterative methods: system of linear equations

[defunc]

Hi all,

I'm looking for a an effective technique for solving a system of linear equations. It should always converge, unlike jacobi or gauss seidel etc. It has to be more efficient than ordinary gauss elimination or kramers rule for large matrices.

Thanks!

 

[arildno]

First off, anything is more efficient than Cramer's Rule!

Secondly, why do you think Gauss elimination is focused so much upon?
It is precisely because it IS the major technique tat always produces convergence.

You may look up into LU-factorization schemes and so on, but typically, these faster (and often preferred) methods will only have conditional convergence.

Simply put, calculation speed is gained by dropping mathematical safe-guards that ensure absolute convergence.

Thus, what you are seeking after is, really, a contradiction in terms.

 

[daniel_i_l]

The more advanced methods usually deal with specific subclasses of matrices. For example, if you're trying to solve symmetric positive-definite systems you might want to look at the conjugate-gradient method:
http://en.wikipedia.org/wiki/Conjugate_gradient_method