Regularization, GSVD and Truncated GSVD (generalized singular value decomposition)

Technical Report · Thu Sep 01 00:00:00 EDT 1988

OSTI ID:6788384

Hansen, P C

The generalized singular value decomposition (GSVD) is used to analyze two alternative methods for solving ill-posed problems: regularization in general form, and truncated SVD. We give conditions in which suitable solutions can be found, discuss the perturbation theory, and show that the optimum regularization and truncation parameters can be computed via generalized cross-validation. Our analysis also sheds light on a particular method, based on a transformation to standard form, that avoids the numerical difficulties associated with computation of the GSVD. 15 refs., 1 fig.

• Research Organization: Oak Ridge National Lab., TN (USA)
• DOE Contract Number: AC05-84OR21400
• OSTI ID: 6788384
• Report Number(s): ORNL/TM-10779; ON: DE88017303
• Resource Relation: Other Information: Portions of this document are illegible in microfiche products
• Country of Publication: United States
• Language: English

Related Subjects

99 GENERAL AND MISCELLANEOUS//MATHEMATICS, COMPUTING, AND INFORMATION SCIENCE
INTEGRAL EQUATIONS
ALGORITHMS
ANALYTICAL SOLUTION
LEAST SQUARE FIT
MATHEMATICS
MATRICES
NUMERICAL SOLUTION
PERTURBATION THEORY
EQUATIONS
MATHEMATICAL LOGIC
MAXIMUM-LIKELIHOOD FIT
990230* - Mathematics & Mathematical Models- (1987-1989)