特異値計算アルゴリズムdLVの基本性質について(応用可積分系, <特集>平成17年研究部会連合発表会)

抄録

Basic propeties of the discrete Lotka-Volterra (dLV) algorithm for computing singular values of bidiagonal matrices are considered. A relative error bound of singular values computed by the dLV algorithm is estimated. The bound is rather smaller than that of the Demmel-Kahan QR algorithm and is in the same level as the qd algorithms. Forward stability and backward stability of the dLV algorithm are also proved. Numerical examples show that the dLV algorithm has a higher relative accuracy. The modified dLV algorithm with shift (mdLVs) algorithm is shown to have quadratic or cubic convergence rate.