Linear systems, Householder reduction
This tutorial discusses Householder reduction of n linear equations to a triangular form which can be solved by back substitution. The main strengths of the method are its numerical stability and suitability for parallel computing. We explain how Householder reduction can be derived from elementary matrix algebra. The method is illustrated by a numerical example and a Pascal algorithm. We assume that the reader has a general knowledge of vector and matrix algebra but is less familiar with linear transformation of a vector space.
Hansen, Per Brinch, "HOUSEHOLDER REDUCTION" (1990). Electrical Engineering and Computer Science Technical Reports. 78.