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A MULTISHIFT, MULTIPOLE RATIONAL QZ METHOD WITHAGGRESSIVE EARLY DEFLATION.
- Source :
- SIAM Journal on Matrix Analysis & Applications; 2021, Vol. 42 Issue 2, p753-774, 22p
- Publication Year :
- 2021
-
Abstract
- n the article "A Rational QZ Method" by D. Camps, K. Meerbergen, and R. Vande-bril [SIAM J. Matrix Anal. Appl., 40 (2019), pp. 943--972], we introduced rational QZ (RQZ) methods. Our theoretical examinations revealed that the convergence of the RQZ method is governed by rational subspace iteration, thereby generalizing the classical QZ method, whose convergence relieson polynomial subspace iteration. Moreover the RQZ method operates on a pencil more general than Hessenberg---upper triangular, namely, a Hessenberg pencil, which is a pencil consisting of two Hessenberg matrices. However, the RQZ method can only be made competitive to advanced QZ implementations by using crucial add-ons such as small bulge multi shift sweeps, aggressive early deflation, and optimal packing. In this paper we develop these techniques for the RQZ method.In the numerical experiments we compare the results with state-of-the-art routines for the generalized eigenvalue problem and show that the presented method is competitive in terms of speed and accuracy. [ABSTRACT FROM AUTHOR]
- Subjects :
- PACKING problem (Mathematics)
PRICE deflation
EIGENVALUES
POLYNOMIALS
PENCILS
Subjects
Details
- Language :
- English
- ISSN :
- 08954798
- Volume :
- 42
- Issue :
- 2
- Database :
- Complementary Index
- Journal :
- SIAM Journal on Matrix Analysis & Applications
- Publication Type :
- Academic Journal
- Accession number :
- 151336930
- Full Text :
- https://doi.org/10.1137/19M1249631