Invert 4x4 matrix - Numerical most stable solution needed

Question

I want to invert a 4x4 matrix. My numbers are stored in fixed-point format (1.15.16 to be exact).

With floating-point arithmetic I usually just build the adjoint matrix

Answer 1

You might consider doubling to 1.31 before doing your normal algorithm. It'll double the number of multiplications, but you're doing a matrix invert and anything you do is going to be pretty tied to the multiplier in your processor.

For anyone interested in finding the equations for a 4x4 invert, you can use a symbolic math package to resolve them for you. The TI-89 will do it even, although it'll take several minutes.

If you give us an idea of what the matrix invert does for you, and how it fits in with the rest of your processing we might be able to suggest alternatives.

-Adam