책 이미지
eBook 미리보기
책 정보
· 제목 : Rank-Deficient and Discrete III-Posed Problems: Numerical Aspects of Linear Inversion (Paperback)
· 분류 : 외국도서 > 과학/수학/생태 > 수학 > 대수학 > 기초대수학
· ISBN : 9780898714036
· 쪽수 : 263쪽
· 출판일 : 1987-01-01
· 분류 : 외국도서 > 과학/수학/생태 > 수학 > 대수학 > 기초대수학
· ISBN : 9780898714036
· 쪽수 : 263쪽
· 출판일 : 1987-01-01
목차
- Preface
- Symbols and Acronyms
- Chapter 1: Setting the Stage. Problems With Ill-Conditioned Matrices
- Ill-Posed and Inverse Problems
- Prelude to Regularization
- Four Test Problems
- Chapter 2: Decompositions and Other Tools. The SVD and its Generalizations
- Rank-Revealing Decompositions
- Transformation to Standard Form
- Computation of the SVE
- Chapter 3: Methods for Rank-Deficient Problems. Numerical Rank
- Truncated SVD and GSVD
- Truncated Rank-Revealing Decompositions
- Truncated Decompositions in Action
- Chapter 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
- Chapter 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
- Chapter 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
- Chapter 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
- Chapter 8. Regularization Tools
- Bibliography
- Index.
