On the numerical stability of Huang's update

Huang's method is a direct method for the solution of linear algebraic equations in which orthogonal projection matrices are used. The error propagation for the zero eigenvalues of these matrices is considered, under suitable hypotheses, in correspondence to four possible update formulas. The analysis performed evidences a calculable parameter which governs the error propagation and confirms theoretically the experimentally observed superiority of the so-called modified version of Huang's method.