The theory of approximate methods and their application to the numerical solution of singular integral equations:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Leyden
Noordhoff
1976
|
| Series: | Monographs and textbooks on mechanics of solids and fluids
2 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Aus dem Russ. übers. |
| Physical Description: | XVII, 330 S. |
| ISBN: | 9028600361 |
Staff View
MARC
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| 240 | 1 | 0 | |a Teorija približennych metodov i ee primenenie k čislennomu rešeniju singuljarnych integral'nych uravnenij |
| 245 | 1 | 0 | |a The theory of approximate methods and their application to the numerical solution of singular integral equations |c V. V. Ivanov. Transl. by A. Ideh. Ed. by R. S. Anderssen ... |
| 264 | 1 | |a Leyden |b Noordhoff |c 1976 | |
| 300 | |a XVII, 330 S. | ||
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| 490 | 1 | |a Monographs and textbooks on mechanics of solids and fluids |v 2 | |
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| 650 | 4 | |a Approximation theory | |
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Record in the Search Index
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|---|---|
| adam_text | CONTENTS
AUTHOR S PREFACE xi
TRANSLATION EDITORS PREFACE xiii
INTRODUCTION xv
CHAPTER 1
METHODS AND ALGORITHMS FOR THE APPROXIMATE SOLUTION
OF GENERAL OPERATOR EQUATIONS
1 RELEVANT ASPECTS OF FUNCTIONAL ANALYSIS 1
1.1 Abstract Spaces 1
1.2 Operators and Functionals 7
1.3 Compact Sets 10
2 THE GENERAL THEORY OF APPROXIMATE METHODS 13
2.1 Linear Problems in a Hilbert Space 13
2.2 Linear Problems in a Banach Space 24
2.3 Non Linear Problems 29
3 THE METHOD OF LEAST SQUARES 41
3.1 The Basis of the Method 41
3.2 An Orthogonalization Algorithm 53
3.3 Gaussian Elimination with Pivoting 59
3.4 A Coordinate wise Descent Algorithm (Gauss Seidel) 69
3.5 The Steepest Descent Algorithm (L.V. Kantorovich) 79
3.6 Some Other Algorithms 84
4 THE RITZ GALERKIN METHOD 86
4.1 Connection with the Method of Least Squares 86
4.2 Properties of the Ritz Galerkin Method 88
5 ITERATIVE METHODS 90
5.1 Simple Iteration and Analytic Continuation 90
5.2 Steepest Descent Methods 102
6 OTHER METHODS AND ALGORITHMS 110
6.1 Yu. V. Vorob ev s Method of Moments 110
6.2 Generalizations of the Method of Least Squares 111
6.3 Some Algorithms for the Solution of Non Linear
Programming Problems 119
6.4 Criteria for the Comparison of Different Algorithms 126
CHAPTER 2
BASIC RESULTS FROM THE THEORY OF ONE DIMENSIONAL
LINEAR SINGULAR INTEGRAL EQUATIONS
7 SINGULAR INTEGRALS AS OPERATORS 131
vii
viii Contents
8 SINGULAR INTEGRAL EQUATIONS WHICH ARE SOLVABLE IN CLOSED FORM 135
8.1 The Dominant Equation in the Case of a Closed Contour 135
8.2 The Dominant Equation in Exceptional Cases 137
8.3 The Dominant Equation in the Case of an Open Contour 140
8.4 A System of Dominant Equations 144
9 THE THEORY OF SINGULAR INTEGRAL EQUATIONS 148
9.1 Basic Concepts 148
9.2 Methods of Regularization 150
9.3 The Integrability and Smoothness of Solutions 152
9.4 Stability of Solutions 153
9.5 A General Functional Approach 157
CHAPTER 3
THE NUMERICAL SOLUTION OF SINGULAR INTEGRAL EQUATIONS
WITH CAUCHY KERNEL
10 RESULTS FROM THE CONSTRUCTIVE THEORY OF FUNCTIONS 161
10.1 Approximation on a Circle 161
10.2 Approximation on Other Sets 167
10.3 Examples of Complete Systems of Functions 169
11 THE APPROXIMATE EVALUATION OF SINGULAR INTEGRALS AND CAUCHY INTEGRALS 172
11.1 Methods Based on the Approximation of the Density Function 172
11.2 Quadrature Formulae 176
11.3 Some Other Methods 182
12 THE CASE OF A NORMALLY SOLVABLE EQUATION WITH CLOSED CONTOUR AND
SUFFICIENTLY SMOOTH INPUT DATA 187
12.1 Application of the Method of Least Squares 187
12.2 Application of the Method of Collocation 191
12.3 Other Methods 199
12.4 The Calculation of Characteristic Values 206
12.5 The Determination of All Solutions 208
13 THE NORMALLY SOLVABLE EQUATION WITH AN OPEN CONTOUR OF INTEGRATION .. 211
13.1 Reduction to the Case of a Closed Contour 211
13.2 Questions on the Improvement of Convergence 213
13.3 Application of the Method of Least Squares 216
14 OTHER CASES OF A SINGLE EQUATION 223
14.1 Equations in the Exceptional Case 223
14.2 Minimum Restrictions on the Smoothness of the Input Data, and on
the Condition for Inversion when a +_ b is zero on y 230
15 SYSTEMS OF SINGULAR INTEGRAL EQUATIONS 233
15.1 Reduction to a System of Fredholm Integral Equations of the
Second Kind 233
15.2 Application of the Method of Least Squares 238
15.3 Application of Iterative Methods 241
15.4 Other Methods 243
Contents i X
16 SYSTEMS OF SINGULAR INTEGRAL EQUATIONS ARISING FROM
QUANTUM FIELD THEORY 248
16.1 Systems of Equations of the First Type 248
16.2 Systems of Equations of the Second Type 250
17 THE COMPUTER SOLUTION OF A SYSTEM ARISING IN DISPERSION THEORY 255
CHAPTER 4
NUMERICAL SOLUTION OF SINGULAR INTEGRAL EQUATIONS
OF CONVOLUTION TYPE
18 THE GENERAL FORM OF SINGULAR INTEGRAL EQUATIONS
OF CONVOLUTION TYPE 265
19 WIENER HOPF EQUATIONS OF THE SECOND KIND 268
20 WIENER HOPF EQUATIONS OF THE FIRST KIND 271
21 APPLICATIONS IN THE THEORY OF AUTOMATIC CONTROL 278
21.1 The Approximate Calculation of Fourier Transforms 278
21.2 Approximation of the Transfer Function 282
21.3 The Determination of the Dynamic Characteristics
of Linear Filters with Constant Parameters 286
21.4 The Numerical Solution of Statistical Linearization
and the Synthesis of Optimum Linear Systems 292
CHAPTER 5
NUMERICAL SOLUTION OF OTHER FORMS OF SINGULAR EQUATIONS
22 INTEGRO DIFFERENTIAL EQUATIONS 303
23 MULTI DIMENSIONAL EQUATIONS 306
24 NON LINEAR EQUATIONS 311
BIBLIOGRAPHY 315
AUTHOR INDEX 325
SUBJECT INDEX 327
|
| any_adam_object | 1 |
| author | Ivanov, Viktor V. 1929- |
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| author_facet | Ivanov, Viktor V. 1929- |
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| author_sort | Ivanov, Viktor V. 1929- |
| author_variant | v v i vv vvi |
| building | Verbundindex |
| bvnumber | BV001966331 |
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| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
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| id | DE-604.BV001966331 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T15:38:03Z |
| institution | BVB |
| isbn | 9028600361 |
| language | English |
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| physical | XVII, 330 S. |
| publishDate | 1976 |
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| publisher | Noordhoff |
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| series | Monographs and textbooks on mechanics of solids and fluids |
| series2 | Monographs and textbooks on mechanics of solids and fluids |
| spelling | Ivanov, Viktor V. 1929- Verfasser (DE-588)129713724 aut Teorija približennych metodov i ee primenenie k čislennomu rešeniju singuljarnych integral'nych uravnenij The theory of approximate methods and their application to the numerical solution of singular integral equations V. V. Ivanov. Transl. by A. Ideh. Ed. by R. S. Anderssen ... Leyden Noordhoff 1976 XVII, 330 S. txt rdacontent n rdamedia nc rdacarrier Monographs and textbooks on mechanics of solids and fluids 2 Aus dem Russ. übers. Équations intégrales - Solutions numériques Approximation theory Integral equations Numerical solutions Numerisches Verfahren (DE-588)4128130-5 gnd rswk-swf Approximationstheorie (DE-588)4120913-8 gnd rswk-swf Singuläre Integralgleichung (DE-588)4181523-3 gnd rswk-swf Integralgleichung (DE-588)4027229-1 gnd rswk-swf Integralgleichung (DE-588)4027229-1 s Approximationstheorie (DE-588)4120913-8 s DE-604 Singuläre Integralgleichung (DE-588)4181523-3 s Numerisches Verfahren (DE-588)4128130-5 s Anderssen, Robert Scott 1939- Sonstige (DE-588)171950798 oth Monographs and textbooks on mechanics of solids and fluids 2 (DE-604)BV001891479 2 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001282359&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Ivanov, Viktor V. 1929- The theory of approximate methods and their application to the numerical solution of singular integral equations Monographs and textbooks on mechanics of solids and fluids Équations intégrales - Solutions numériques Approximation theory Integral equations Numerical solutions Numerisches Verfahren (DE-588)4128130-5 gnd Approximationstheorie (DE-588)4120913-8 gnd Singuläre Integralgleichung (DE-588)4181523-3 gnd Integralgleichung (DE-588)4027229-1 gnd |
| subject_GND | (DE-588)4128130-5 (DE-588)4120913-8 (DE-588)4181523-3 (DE-588)4027229-1 |
| title | The theory of approximate methods and their application to the numerical solution of singular integral equations |
| title_alt | Teorija približennych metodov i ee primenenie k čislennomu rešeniju singuljarnych integral'nych uravnenij |
| title_auth | The theory of approximate methods and their application to the numerical solution of singular integral equations |
| title_exact_search | The theory of approximate methods and their application to the numerical solution of singular integral equations |
| title_full | The theory of approximate methods and their application to the numerical solution of singular integral equations V. V. Ivanov. Transl. by A. Ideh. Ed. by R. S. Anderssen ... |
| title_fullStr | The theory of approximate methods and their application to the numerical solution of singular integral equations V. V. Ivanov. Transl. by A. Ideh. Ed. by R. S. Anderssen ... |
| title_full_unstemmed | The theory of approximate methods and their application to the numerical solution of singular integral equations V. V. Ivanov. Transl. by A. Ideh. Ed. by R. S. Anderssen ... |
| title_short | The theory of approximate methods and their application to the numerical solution of singular integral equations |
| title_sort | the theory of approximate methods and their application to the numerical solution of singular integral equations |
| topic | Équations intégrales - Solutions numériques Approximation theory Integral equations Numerical solutions Numerisches Verfahren (DE-588)4128130-5 gnd Approximationstheorie (DE-588)4120913-8 gnd Singuläre Integralgleichung (DE-588)4181523-3 gnd Integralgleichung (DE-588)4027229-1 gnd |
| topic_facet | Équations intégrales - Solutions numériques Approximation theory Integral equations Numerical solutions Numerisches Verfahren Approximationstheorie Singuläre Integralgleichung Integralgleichung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001282359&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV001891479 |
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