On the Convergence of an Implicitly Restarted Arnoldi Method

Journal Article · Mon Jul 12 00:00:00 EDT 1999 · SIAM Journal on Matrix Analysis and Its Applications

OSTI ID:9021

Lehoucq, Richard B

We show that Sorensen's [35] implicitly restarted Arnoldi method (including its block extension) is simultaneous iteration with an implicit projection step to accelerate convergence to the invariant subspace of interest. By using the geometric convergence theory for simultaneous iteration due to Watkins and Elsner [43], we prove that an implicitly restarted Arnoldi method can achieve a super-linear rate of convergence to the dominant invariant subspace of a matrix. Moreover, we show how an IRAM computes a nested sequence of approximations for the partial Schur decomposition associated with the dominant invariant subspace of a matrix.

• Research Organization: Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Sandia National Lab. (SNL-CA), Livermore, CA (United States)
• Sponsoring Organization: US Department of Energy (US)
• DOE Contract Number: AC04-94AL85000
• OSTI ID: 9021
• Report Number(s): SAND99-1756J; TRN: AH200122%%138
• Journal Information: SIAM Journal on Matrix Analysis and Its Applications, Other Information: Submitted to SIAM Journal on Matrix Analysis and Its Applications; PBD: 12 Jul 1999
• Country of Publication: United States
• Language: English

Related Subjects

99 GENERAL AND MISCELLANEOUS//MATHEMATICS, COMPUTING, AND INFORMATION SCIENCE
CONVERGENCE
EIGENVALUES
ITERATIVE METHODS
MATRIX ELEMENTS
SIMULTANEOUS ITERATION
ARNOLDI REDUCTION
SCHUR DECOMPOSITION
RESTARTING
EIGEN-VALUES