Asymptotic Analysis of a New Multishift QR Method for Symmetric Tridiagonal Eigenproblems(Theory,Aigorithms for Matrix/Eigenvalue Problems and their Applications,<Special Issue>Joint Symposium of JSIAM Activity Groups 2008)

Abstract

The Multishift QR method (M-QR) enables us to compute all the eigenvalues of a symmetric tridiagonal matrix on parallel machines. To use all processors sufficiently, the Deferred shift QR method (D-QR) is proposed. However, the convergence rate of D-QR is numerically inferior to that of M-QR. Recently, the Fully Pipelined Multishift QR method (FPM-QR) is proposed. FPM-QR shows better convergence than D-QR while keeping the high level of processor utilization. In this paper, we analyze the asymptotic behavior of FPM-QR with two shifts.