Rank-deficient and discrete ill-posed problems: numerical aspects of linear inversion
Saved in:
| Main Author: | |
|---|---|
| Format: | Electronic eBook |
| Language: | English |
| Published: |
Philadelphia, Pa.
Society for Industrial and Applied Mathematics (SIAM, 3600 Market Street, Floor 6, Philadelphia, PA 19104)
1998
|
| Series: | SIAM monographs on mathematical modeling and computation
4 |
| Subjects: | |
| Links: | https://doi.org/10.1137/1.9780898719697 https://doi.org/10.1137/1.9780898719697 https://doi.org/10.1137/1.9780898719697 https://doi.org/10.1137/1.9780898719697 https://doi.org/10.1137/1.9780898719697 |
| Item Description: | Mode of access: World Wide Web. - System requirements: Adobe Acrobat Reader Includes bibliographical references (s. 215-242) and index 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 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 |
| Physical Description: | 1 Online-Ressource (xvi, 247 Seiten) |
| ISBN: | 0898714036 9780898714036 |
| DOI: | 10.1137/1.9780898719697 |
Staff View
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| 500 | |a 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 | ||
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| id | DE-604.BV039747138 |
| illustrated | Not Illustrated |
| indexdate | 2024-12-20T16:01:24Z |
| institution | BVB |
| isbn | 0898714036 9780898714036 |
| language | English |
| lccn | 97032066 |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-024594668 |
| oclc_num | 873886047 |
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| owner | DE-91 DE-BY-TUM DE-29 DE-706 DE-83 DE-20 |
| owner_facet | DE-91 DE-BY-TUM DE-29 DE-706 DE-83 DE-20 |
| physical | 1 Online-Ressource (xvi, 247 Seiten) |
| psigel | ZDB-72-SIA |
| publishDate | 1998 |
| publishDateSearch | 1998 |
| publishDateSort | 1998 |
| publisher | Society for Industrial and Applied Mathematics (SIAM, 3600 Market Street, Floor 6, Philadelphia, PA 19104) |
| record_format | marc |
| series | SIAM monographs on mathematical modeling and computation |
| series2 | SIAM monographs on mathematical modeling and computation |
| spellingShingle | Hansen, Per Christian 1957- Rank-deficient and discrete ill-posed problems numerical aspects of linear inversion SIAM monographs on mathematical modeling and computation Equations, Simultaneous / Numerical solutions Iterative methods (Mathematics) Sparse matrices Numerische lineare Algebra (DE-588)1172564329 gnd Inkorrekt gestelltes Problem (DE-588)4186951-5 gnd Numerisches Verfahren (DE-588)4128130-5 gnd |
| subject_GND | (DE-588)1172564329 (DE-588)4186951-5 (DE-588)4128130-5 |
| title | Rank-deficient and discrete ill-posed problems numerical aspects of linear inversion |
| title_auth | Rank-deficient and discrete ill-posed problems numerical aspects of linear inversion |
| title_exact_search | Rank-deficient and discrete ill-posed problems numerical aspects of linear inversion |
| title_full | Rank-deficient and discrete ill-posed problems numerical aspects of linear inversion Per Christian Hansen |
| title_fullStr | Rank-deficient and discrete ill-posed problems numerical aspects of linear inversion Per Christian Hansen |
| title_full_unstemmed | Rank-deficient and discrete ill-posed problems numerical aspects of linear inversion Per Christian Hansen |
| title_short | Rank-deficient and discrete ill-posed problems |
| title_sort | rank deficient and discrete ill posed problems numerical aspects of linear inversion |
| title_sub | numerical aspects of linear inversion |
| topic | Equations, Simultaneous / Numerical solutions Iterative methods (Mathematics) Sparse matrices Numerische lineare Algebra (DE-588)1172564329 gnd Inkorrekt gestelltes Problem (DE-588)4186951-5 gnd Numerisches Verfahren (DE-588)4128130-5 gnd |
| topic_facet | Equations, Simultaneous / Numerical solutions Iterative methods (Mathematics) Sparse matrices Numerische lineare Algebra Inkorrekt gestelltes Problem Numerisches Verfahren |
| url | https://doi.org/10.1137/1.9780898719697 |
| volume_link | (DE-604)BV047220660 |
| work_keys_str_mv | AT hansenperchristian rankdeficientanddiscreteillposedproblemsnumericalaspectsoflinearinversion |