An algorithm to solve some symmetric eigenvalue problem

Аuthors

Tyutyunnikov N. P.^1*, Shalashilin V. I.²

1. Institute of Applied Mechanics of Russian Academy of Science, IAM RAS, 32a, Leninskii av., Moscow, В-334, GSP-1, 119991, Russia
2. Moscow Aviation Institute (National Research University), 4, Volokolamskoe shosse, Moscow, А-80, GSP-3, 125993, Russia

*e-mail: nicpet@list.ru

Abstract

A new algorithm is suggested to solve classical eigenvalue problem for a real symmetric matrix. The algorithm is based on solving of recurrent sequence of reduced problems with increasing order. A reduction basis used in the algorithm is generated for each subsequent problem within the sequence based on proper basis of preceding problem in the same sequence by means of addition of a new basic vector to it. Features of the algorithm are considered for a case of multiple roots. The algorithm offered is compared with some other algorithms for the same problem. According test results the algorithm offered is worse slightly in comparison with the QR- algorithm, but more suitable for parallel computation processes.