ANSI C - Numerically Stable Reverse Substitution Algorithm for Upper Right Triangular Matrices

Question

I am performing matrix inversion using Householder transformations acting on the extended matrix. Currently, I can only perform exact inversions for matrix sizes up to 4x4. After that, A * A ^ -1! = I’m for sure, and I think this is due to reverse substitution.

Is there a better way to do this?

Answer 1

It turns out that the viability of the method of "Domholder with reverse replacement". When verifying that the row has zeros at the correct locations, which should be part of the matrix in the form of a line-level, it is important to compare both the real and imaginary components of the matrix notation with zero, and not their size.