Evaluation of a New Eigen Decomposition Algorithm for Symmetric Tridiagonal Matrices
Hiroaki Tsuboi, Taro Konda, Masami Takata, Kinji Kimura, Masashi Iwasaki, Yoshimasa Nakamura · 2006
Abstract This paper focuses on a new extension version of double Divide and Conquer (dDC) algorithm to eigen decomposition. Recently, dDC was proposed for singular value decomposition (SVD) of rectangular matrix. The dDC for SVD consists of two parts. One is Divide and Conquer (D&C) for singular value and the other is twisted factorization for singular vector. The memory usage of dDC is smaller than that of D&C. Both theoretical and running time are also shorter than those of D&C. In this paper, a new dDC for eigen decomposition is proposed. A shift of origin is introduced into our dDC. By some numerical tests, dDC is evaluated with respect to running time and accuracy.