Small size linear solver

Linear solver of multiple 2x2 and 3x3 systems

Description

Solve multiple (2x2) or (3x3) linear systems:

A(:,:,k)*X(:,:,k) = B(:,:,k) for k=1,2,...,N

The method used here is basic cofactor/determinant.

DISADVANTAGE: This method may be less accurate than Matlab backslash (using in for-loop) when the matrices are ill-conditioned.

ADVANTAGE: for a large number of systems - the speed-up is about 15-30 fold.

Acknowledgements

The author wishes to acknowledge the following in the creation of this submission:
MTIMESX - Fast Matrix Multiply with Multi-Dimensional Support

• MATLAB release: MATLAB 7.10 (2010a)

[Yvan Lengwiler]

Bruno, I tried to run your benchmark file (bench_inv2inv3.m) but ended up with an error:
??? Undefined function or method 'mtimesx' ...
A file seems to be missing.

[Yvan Lengwiler]

Bruno. Please ignore my previous comment. I overlooked that another MathCentral submission is required for your program to run.

[James Tursa]

FYI, I just uploaded a new version of MTIMESX that does small matrix multiplies (first two dimensions <= 4) with inline code in 'SPEED' mode. This runs faster than the previous version.