Uniform accuracy of eigenpairs from a shift-invert Lanczos method.

Journal Article · Fri Apr 01 04:00:00 EST 2005 · Proposed for publication in the SIAM Journal on Matrix Analysis and Applications Special Issue on Accurate Solution of Eigenvalue P.

OSTI ID:972461

Lehoucq, Richard B; Hetmaniuk, Ulrich L

This paper analyzes the accuracy of the shift-invert Lanczos iteration for computing eigenpairs of the symmetric definite generalized eigenvalue problem. We provide bounds for the accuracy of the eigenpairs produced by shift-invert Lanczos given a residual reduction. We discuss the implications of our analysis for practical shift-invert Lanczos iterations. When the generalized eigenvalue problem arises from a conforming finite element method, we also comment on the uniform accuracy of bounds (independent of the mesh size h).

• Research Organization: Sandia National Laboratories
• Sponsoring Organization: USDOE
• DOE Contract Number: AC04-94AL85000
• OSTI ID: 972461
• Report Number(s): SAND2005-2588J
• Journal Information: Proposed for publication in the SIAM Journal on Matrix Analysis and Applications Special Issue on Accurate Solution of Eigenvalue P., Journal Name: Proposed for publication in the SIAM Journal on Matrix Analysis and Applications Special Issue on Accurate Solution of Eigenvalue P.
• Country of Publication: United States
• Language: English

Related Subjects

97 MATHEMATICS AND COMPUTING
99 GENERAL AND MISCELLANEOUS
ACCURACY
BOUNDARY CONDITIONS
EIGENVALUES
FINITE ELEMENT METHOD
ITERATIVE METHODS