A study on modified biorthogonalization method for decreasing a breakdown condition
Sun Kyung Kim · Journal of the Korea Industrial Information Systems Research · 2002
Many important scientific and engineering problems require the computation of a small number of eigenvalues for large nonsymmetric matrices. The biorthogonal Lanczos method is one of the methods to solve that problem, but it faces serious breakdown problems. In this paper, we introduce a modified biorthogonal Lanczos method to find a few eigenvalues of a large sparse nonsymmetric matrix. The proposed method generates reduction matrices that are similar to those generated by the standard biorthogonal Lanczos method. We prove that the breakdown conditions of our method are less stringent than the standard method. We then implement the modified biorthogonal Lanczos method on the CRAY machine and discuss the decreased breakdown conditions.