Rank-Deficient and Discrete Ill-Posed Problems: Numerical Aspects of Linear Inversion - Brossura

Hansen, Per Christian

Brossura

ISBN 10: 0898714036 ISBN 13: 9780898714036

Casa editrice: Society for Industrial and Applied Mathematics, 1997

Riassunto

An overview of modern computational stabilization methods for linear inversion: applications to audio processing, medical imaging, seismology and other areas.

Su questo libro

Descrizione del libro

Here is an overview of modern computational stabilization methods for linear inversion, with applications to a variety of problems in audio processing, medical imaging, tomography, seismology, astronomy, and other areas.

Contenuti

Preface; Symbols and Acronyms; 1. Setting the Stage. Problems With Ill-Conditioned Matrices; Ill-Posed and Inverse Problems; Prelude to Regularization; Four Test Problems; 2. Decompositions and Other Tools. The SVD and its Generalizations; Rank-Revealing Decompositions; Transformation to Standard Form; Computation of the SVE; 3. Methods for Rank-Deficient Problems. Numerical Rank; Truncated SVD and GSVD; Truncated Rank-Revealing Decompositions; Truncated Decompositions in Action; 4. Problems with Ill-Determined Rank. Characteristics of Discrete Ill-Posed Problems; Filter Factors; Working with Seminorms; The Resolution Matrix, Bias, and Variance; The Discrete Picard Condition; L-Curve Analysis; Random Test Matrices for Regularization Methods; The Analysis Tools in Action; 5. Direct Regularization Methods. Tikhonov Regularization; The Regularized General Gauss–Markov Linear Model; Truncated SVD and GSVD Again; Algorithms Based on Total Least Squares; Mollifier Methods; Other Direct Methods; Characterization of Regularization Methods; Direct Regularization Methods in Action; 6. Iterative Regularization Methods. Some Practicalities; Classical Stationary Iterative Methods; Regularizing CG Iterations; Convergence Properties of Regularizing CG Iterations; The LSQR Algorithm in Finite Precision; Hybrid Methods; Iterative Regularization Methods in Action; 7. Parameter-Choice Methods. Pragmatic Parameter Choice; The Discrepancy Principle; Methods Based on Error Estimation; Generalized Cross-Validation; The L-Curve Criterion; Parameter-Choice Methods in Action; Experimental Comparisons of the Methods; 8. Regularization Tools; Bibliography; Index.

Dettagli dell'edizione

• Editore: Society for Industrial and Applied Mathematics
• Data di pubblicazione: 1997
• Lingua: Inglese
• ISBN 10: 0898714036
• ISBN 13: 9780898714036
• Rilegatura: Copertina flessibile
• Numero di pagine: 263
• Contatto del produttore: non disponibile
• Persona responsabile: Mare Nostrum Group B.V.; gpsr@mare-nostrum.co.uk; ; Doelen 72; Breda; 4831 GR; Paesi Bassi