Year: 2012
Type: preprint
Abstract: We present a new transform, triple dqds, to help to compute the eigenvalues of a real tridiagonal matrix C using real arithmetic. The algorithm uses the real dqds transform to shift by a real number and triple dqds to shift by a complex conjugate pair. We present what seems to be a new criteria for splitting the current pair L,U. The algorithm rejects any transform which suffers from excessive element growth and then tries a new transform. Our numerical tests show that the algorithm is about 100 times faster than the Ehrlich-Aberth method of D. A. Bini, L. Gemignani and F. Tisseur. Our code is comparable in performance to a complex dqds code and is sometimes 3 times faster.
Source: arXiv (Cornell University)
Authors: Ferreira, Carla, Parlett, Beresford
Institutions: University of Minho, University of California, Berkeley
Language: English
Topic: Matrix Theory and Algorithms
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
Award: G1578237752
OpenAlex ID: W122382533