Improvement of Divide and Conquer Algorithm by Twisted Factorization for Eigenvalue Decomposition(Algorithms for Matrix/Eigenvalue Problems and their Applications,<Special Issue>Joint Symposium of JSIAM Activity Groups 2008)

Abstract

An algorithm which consists of a simplified D & C and twisted factorization is proposed for symmetric tridiagonal eigenvalue decomposition. The complexity is O(n^2) and the memory usage is O(n) if no cluster exists. The orthogonality can be improved by additional one step of the inverse iteration, although the classical D & C shows better one. In some numerical tests, our algorithm shows stable speed and better accuracy of the decompositions. But the orthogonality is worse than those of the classical D & C in up to three digits.