Solutions of ill-posed problems:
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English Russian |
| Published: |
Washington, DC
Winston
1977
|
| Series: | Scripta series in mathematics.
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | EST: Metody rešenija nekorrektnych zadač (engl.) |
| Physical Description: | XIII, 258 S. graph. Darst. |
| ISBN: | 0470991240 |
Staff View
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| 245 | 1 | 0 | |a Solutions of ill-posed problems |c Andrej N. Tichonov ; Vasilij J. Arsenin* |
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Record in the Search Index
| _version_ | 1804116419057549312 |
|---|---|
| adam_text | CONTENTS
TRANSLATION EDITOR S PREFACE ix
PREFACE TO THE ENGLISH EDITION xi
INTRODUCTION 1
§ 1. Remarks on the formulation of mathematical problems 1
§2. The concepts of well posed and ill posed problems ... 7
§3. Examples of ill posed problems 9
CHAPTER L THE SELECTION METHOD. QUASISOLUTIONS 27
§1. The selection method of solving ill posed problems ... 28
§2. Quasisolutions 32
§3. Approximate determination of quasisolutions 37
§4. Replacement of the question Az = u with an equation
close to it 40
§5. The method of quasiinversion 42
CHAPTER II. THE REGULARIZATION METHOD 45
§ 1. The concept of a regularizing operator 45
§2. Methods of constructing regularizing operators 50
§3. The construction of regularizing operators by
minimization of a smoothing funcational 63
§4. Application of the regularization method to the ap¬
proximate solution of integral equations of the first
kind 73
§5. Examples of application of the regularization method . 78
§6. Determination of the regularization parameter 87
v
CHAPTER III. SOLUTION OF SINGULAR AND ILL CONDI¬
TIONED SYSTEMS OF LINEAR ALGEBRAIC
EQUATIONS 95
§ 1. The regularization method of finding the normal
solution 99
§2. Supplementary remarks 107
CHAPTER IV. APPROXIMATE SOLUTIONS OF INTEGRAL
EQUATIONS OF THE FIRST KIND OF THE
CONVOLUTION TYPE 109
§ 1. Classes of regularizing operators for equations of the
convolution type 110
§2. Deviation of the regularized solution from the exact
one 124 I
§3. Asymptotic estimates of the deviation of a regularized
solution from the exact solution for an equation of i
the convolution type as a *¦ 0 129
CHAPTER V. CERTAIN OPTIMAL REGULARIZING
OPERATORS FOR INTEGRAL EQUATIONS
OF THE CONVOLUTION TYPE 147
§ 1. The optimal regularized solution. The connection
between the regularization method and optimal Wiener
filtering 149
§2. Properties of the function p(p) for equations with
kernels of types I IV 155
§3. Determination of the high frequency characteristics of
a signal and noise and of the optimal value of the
regularization parameter 164
CHAPTER VI. STABLE METHODS OF SUMMING FOURIER
SERIES WITH COEFFICIENTS THAT ARE
APPROXIMATE IN THE l2 METRIC 175
§ 1. Classes of stable methods of summing Fourier series .177
§2. Optimal methods of summing Fourier series 187
vi
CHAPTER VII. STABLE METHODS OF MINIMIZING
FUNCTIONALS AND SOLVING OPTIMAL
CONTROL PROBLEMS 191
§1. A stable method of minimizing functionals 194
i §2. A stable method of solving optimal control problems . 202
!
, CHAPTER VIII. STABLE METHODS OF SOLVING OPTIMAL
I PLANNING (LINEAR PROGRAMMING)
PROBLEMS 211
§ 1. The formulation of optimal planning and mathemati¬
cal programming problems 212
§2. Optimal planning problems. Existence and uniqueness
of solutions 216
§3. The regularization method of solving optimal
planning problems 222
BIBLIOGRAPHY 236
SUBJECT INDEX 256
vii
|
| any_adam_object | 1 |
| author | Tichonov, Andrej N. Arsenin, Vasilij J. |
| author_facet | Tichonov, Andrej N. Arsenin, Vasilij J. |
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| author_sort | Tichonov, Andrej N. |
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| building | Verbundindex |
| bvnumber | BV001974723 |
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| callnumber-raw | QA297 |
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| callnumber-subject | QA - Mathematics |
| classification_rvk | SK 640 SK 900 SK 920 |
| ctrlnum | (OCoLC)2837312 (DE-599)BVBBV001974723 |
| dewey-full | 519.4 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 519 - Probabilities and applied mathematics |
| dewey-raw | 519.4 |
| dewey-search | 519.4 |
| dewey-sort | 3519.4 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| illustrated | Illustrated |
| indexdate | 2024-07-09T15:38:12Z |
| institution | BVB |
| isbn | 0470991240 |
| language | English Russian |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-001287984 |
| oclc_num | 2837312 |
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| physical | XIII, 258 S. graph. Darst. |
| publishDate | 1977 |
| publishDateSearch | 1977 |
| publishDateSort | 1977 |
| publisher | Winston |
| record_format | marc |
| series2 | Scripta series in mathematics. |
| spelling | Tichonov, Andrej N. Verfasser aut Metody rešenija nekor rektnych zadač Solutions of ill-posed problems Andrej N. Tichonov ; Vasilij J. Arsenin* Washington, DC Winston 1977 XIII, 258 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Scripta series in mathematics. EST: Metody rešenija nekorrektnych zadač (engl.) Analyse numérique - Problèmes mal posés Mathématiques - Problèmes et exercices Résolution de problème Numerical analysis Improperly posed problems Integralgleichung (DE-588)4027229-1 gnd rswk-swf Näherungsverfahren (DE-588)4206467-3 gnd rswk-swf Operatorgleichung (DE-588)4043601-9 gnd rswk-swf Operatorgleichung (DE-588)4043601-9 s Näherungsverfahren (DE-588)4206467-3 s DE-604 Integralgleichung (DE-588)4027229-1 s Arsenin, Vasilij J. Verfasser aut HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001287984&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Tichonov, Andrej N. Arsenin, Vasilij J. Solutions of ill-posed problems Analyse numérique - Problèmes mal posés Mathématiques - Problèmes et exercices Résolution de problème Numerical analysis Improperly posed problems Integralgleichung (DE-588)4027229-1 gnd Näherungsverfahren (DE-588)4206467-3 gnd Operatorgleichung (DE-588)4043601-9 gnd |
| subject_GND | (DE-588)4027229-1 (DE-588)4206467-3 (DE-588)4043601-9 |
| title | Solutions of ill-posed problems |
| title_alt | Metody rešenija nekor rektnych zadač |
| title_auth | Solutions of ill-posed problems |
| title_exact_search | Solutions of ill-posed problems |
| title_full | Solutions of ill-posed problems Andrej N. Tichonov ; Vasilij J. Arsenin* |
| title_fullStr | Solutions of ill-posed problems Andrej N. Tichonov ; Vasilij J. Arsenin* |
| title_full_unstemmed | Solutions of ill-posed problems Andrej N. Tichonov ; Vasilij J. Arsenin* |
| title_short | Solutions of ill-posed problems |
| title_sort | solutions of ill posed problems |
| topic | Analyse numérique - Problèmes mal posés Mathématiques - Problèmes et exercices Résolution de problème Numerical analysis Improperly posed problems Integralgleichung (DE-588)4027229-1 gnd Näherungsverfahren (DE-588)4206467-3 gnd Operatorgleichung (DE-588)4043601-9 gnd |
| topic_facet | Analyse numérique - Problèmes mal posés Mathématiques - Problèmes et exercices Résolution de problème Numerical analysis Improperly posed problems Integralgleichung Näherungsverfahren Operatorgleichung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001287984&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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