A primer on integral equations of the first kind: the problem of deconvolution and unfolding
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Philadelphia
Soc. for Industrial and Applied Mathematics
1991
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XIV, 135 S. graph. Darst. |
| ISBN: | 0898712637 |
Staff View
MARC
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| 245 | 1 | 0 | |a A primer on integral equations of the first kind |b the problem of deconvolution and unfolding |c G. Milton Wing |
| 264 | 1 | |a Philadelphia |b Soc. for Industrial and Applied Mathematics |c 1991 | |
| 300 | |a XIV, 135 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
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| 650 | 4 | |a Transport | |
| 650 | 4 | |a Équations intégrales | |
| 650 | 4 | |a Integral equations | |
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Record in the Search Index
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| adam_text | Contents
Preface ix
1 An Introduction to the Basic Problem 1
1.1 The Problem Posed 1
1.2 Interpretation of Integral Equations of the First Kind . . 3
1.3 Some Ground Rules 3
1.4 A Minor Difficulty Overcome 4
1.5 Summary 4
Problems I 5
2 Some Examples 7
2.1 Introduction 7
2.2 The Laplace Transform 7
2.3 Some Remarks About Transport Theory 8
2.4 Determination of a Signal by Absorption—Slab Geometry 9
2.5 X Ray Determination of the Density Distribution in a
Sphere—PHERMEX Problem 11
2.6 The Problem of Tomography 13
2.7 Determination of Source Strength in an Absorbing
Material 15
2.8 Determination of the Radial Density Distribution of
Plutonium in a Small Sphere 16
2.9 A Problem in Geomagnetic Prospecting 17
2.10 A Problem for the Department of Game and Fish 18
vii
viii Contents
2.11 A Problem in Mechanics 19
2.12 Some Observations and an Important Concept 21
2.13 Summary 22
Problems II „ 22
3 A Bit of Functional Analysis 27
3.1 Introduction 27
3.2 Norms of Functions 27
3.3 Norms of Vectors 29
3.4 Norms of Integral Operators 30
3.5 Norms of Differential Operators 32
3.6 Norms of Matrix Operators 35
3.7 Norms of General Operators T 36
3.8 Summary 37
Problems III 38
4 Integral Operators with Separable Kernels 41
4.1 Introduction 41
4.2 Separable Kernels 41
4.3 Some Properties of Integral Operators with Separable
Kernels 42
4.4 IFKs with Separable Kernels 43
4.5 Eigenvalues and Eigenfunctions of Integral Operators with
Separable Kernels 45
4.6 Integral Equations of the Second Kind with Separable
Kernels 46
4.7 Summary 48
Problems IV 48
5 Integral Operators with General Kernels 51
5.1 Introduction 51
5.2 Some More Facts About Integral Operators—Existence
and Boundedness of Inverses 52
5.3 Eigenvalues and Eigenfunctions of Integral Operators with
Symmetric Kernels 56
5.4 Eigenvalues and Eigenfunctions of Nonsymmetric
Operators—Singular Values and Singular Functions ... 58
5.5 Integral Equations of the Second Kind with Symmetric
Kernels 63
Contents ix
5.6 Integral Equations of the First Kind with General Kernels 65
5.7 Summary 66
Problems V 67
6 Some Methods of Resolving Integral Equations of the
First Kind 71
6.1 Introduction 71
6.2 Classical Quadrature Approach 72
6.2.1 Basic Scheme 72
6.2.2 A Particular Application of the Quadrature
Approach 73
6.2.3 A Trivial Example and Some Important
Observations 76
6.2.4 Section 6.2.2 Revisited 78
6.2.5 A Return to the Kernel K = 1 + r/xy 78
6.2.6 The Condition Number of a Matrix 79
6.2.7 A Digression Concerning Approximate Kernels . . 80
6.2.8 The Method of Least Squares 81
6.2.9 Some Miscellaneous Comments Concerning the
Quadrature Method 83
6.2.10 A Summary of the Classical Quadrature Approach 85
6.3 General Series Expansions 85
6.3.1 Basic Scheme 85
6.3.2 Series Expansions and Projection and Collocation
Methods 87
6.4 Expansion in Series of Eigenfunctions and Singular
Functions 89
6.4.1 Basic Scheme 89
6.4.2 A Variant of the Method 90
6.5 Parametrized Solution Function Method 91
6.6 The Method of Regularization 92
6.6.1 Some Background and the Basic Scheme 92
6.6.2 Some Numerical Examples 97
6.6.3 The Selection of the Parameter, 7 103
6.6.4 A Generalization of the Concept of Regularization 103
6.7 Stochastic Approaches 103
6.8 Iterative Methods 106
6.9 Summary 107
Problems VI 107
x Contents
7 Some Important Miscellany 113
7.1 Introduction 113
7.2 About Those Ground Rules 113
7.3 A Final Word About Codes and Quadrature Schemes . . 114
7.4 Finding Generalized Moments of Solutions 115
7.5 IFKs in More Variables 116
7.6 Errors in the Kernel 117
7.7 Summary 117
Problems VII 117
8 Epilogue 119
References 121
Appendix A 125
Appendix B 127
Appendix C 129
Index 133
|
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| dewey-ones | 515 - Analysis |
| dewey-raw | 515/.45 |
| dewey-search | 515/.45 |
| dewey-sort | 3515 245 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
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| id | DE-604.BV009264281 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T17:34:08Z |
| institution | BVB |
| isbn | 0898712637 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-006165499 |
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| physical | XIV, 135 S. graph. Darst. |
| publishDate | 1991 |
| publishDateSearch | 1991 |
| publishDateSort | 1991 |
| publisher | Soc. for Industrial and Applied Mathematics |
| record_format | marc |
| spelling | Wing, George Milton 1923-2008 Verfasser (DE-588)11953987X aut A primer on integral equations of the first kind the problem of deconvolution and unfolding G. Milton Wing Philadelphia Soc. for Industrial and Applied Mathematics 1991 XIV, 135 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Equation intégrale première espèce Equations intégrales ram Transport Équations intégrales Integral equations Fredholm-Integralgleichung (DE-588)4155261-1 gnd rswk-swf Lineare Integralgleichung (DE-588)4114426-0 gnd rswk-swf (DE-588)4151278-9 Einführung gnd-content Fredholm-Integralgleichung (DE-588)4155261-1 s DE-604 Lineare Integralgleichung (DE-588)4114426-0 s HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006165499&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Wing, George Milton 1923-2008 A primer on integral equations of the first kind the problem of deconvolution and unfolding Equation intégrale première espèce Equations intégrales ram Transport Équations intégrales Integral equations Fredholm-Integralgleichung (DE-588)4155261-1 gnd Lineare Integralgleichung (DE-588)4114426-0 gnd |
| subject_GND | (DE-588)4155261-1 (DE-588)4114426-0 (DE-588)4151278-9 |
| title | A primer on integral equations of the first kind the problem of deconvolution and unfolding |
| title_auth | A primer on integral equations of the first kind the problem of deconvolution and unfolding |
| title_exact_search | A primer on integral equations of the first kind the problem of deconvolution and unfolding |
| title_full | A primer on integral equations of the first kind the problem of deconvolution and unfolding G. Milton Wing |
| title_fullStr | A primer on integral equations of the first kind the problem of deconvolution and unfolding G. Milton Wing |
| title_full_unstemmed | A primer on integral equations of the first kind the problem of deconvolution and unfolding G. Milton Wing |
| title_short | A primer on integral equations of the first kind |
| title_sort | a primer on integral equations of the first kind the problem of deconvolution and unfolding |
| title_sub | the problem of deconvolution and unfolding |
| topic | Equation intégrale première espèce Equations intégrales ram Transport Équations intégrales Integral equations Fredholm-Integralgleichung (DE-588)4155261-1 gnd Lineare Integralgleichung (DE-588)4114426-0 gnd |
| topic_facet | Equation intégrale première espèce Equations intégrales Transport Équations intégrales Integral equations Fredholm-Integralgleichung Lineare Integralgleichung Einführung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006165499&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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