Analysis of the Diagonal Pivoting Method
James R. Bunch · SIAM Journal on Numerical Analysis · 1971
A backwards error analysis of the diagonal pivoting method for solving symmetric (indefinite) systems of linear equations shows that the elements of the associated error matrix can be bounded in terms of the elements of the reduced matrices. The elements of the reduced matrices are shown to be bounded by $3nf(n)$ for a symmetric nonsingular system of order n, in contrast to the bound $\sqrt n f(n)$ which has been obtained for Gaussian elimination with complete pivoting. An operation count shows that the number of multiplications, additions, and comparisons is at most of the order ${{n^3 } / 6}$ for each. The results also hold for Hermitian systems.