Approximate solutions of operator equations:
Gespeichert in:
| Beteiligte Personen: | , , |
|---|---|
| Format: | Buch |
| Sprache: | Englisch |
| Veröffentlicht: |
Singapore [u.a.]
World Scientific
1997
|
| Schriftenreihe: | Series in approximations and decompositions
9 |
| Schlagwörter: | |
| Links: | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007932378&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| Umfang: | XIII, 343 S. graph. Darst. |
| ISBN: | 9810230648 |
Internformat
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| 245 | 1 | 0 | |a Approximate solutions of operator equations |c Mingjun Chen ; Zhongying Chen ; Guanrong Chen |
| 264 | 1 | |a Singapore [u.a.] |b World Scientific |c 1997 | |
| 300 | |a XIII, 343 S. |b graph. Darst. | ||
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| 337 | |b n |2 rdamedia | ||
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| 490 | 1 | |a Series in approximations and decompositions |v 9 | |
| 650 | 4 | |a Approximation theory | |
| 650 | 4 | |a Operator equations |x Numerical solutions | |
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Datensatz im Suchindex
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|---|---|
| adam_text | Contents
Preface vii
Chapter 1 Introduction 1
1.1 Overview of Different Approximation Methods 2
1.2 Projection Operators and Their Properties 6
1.3 Projective Approximation Algorithms (I) 7
1.4 Projective Approximation Algorithms (II) 12
1.5 Examples of Projective Approximation Methods 16
Exercises 21
Chapter 2 Operator Equations and Their Approximate
Solutions (I): Compact Linear Operators 27
2.1 Compact Operators and Their Equations 28
2.2 Projection Algorithms: The Banach Space Setting 32
2.3 Approximate Solutions of Predholm Integral Equation and Boundary
Value Problems of Higher Order Ordinary Differential Equations .. 36
2.3.1 Fredholm integral equation and its approximate solutions 36
2.3.2 Approximate solutions for boundary value problems of
higher order ordinary differential equations 42
2.4 Projection Algorithms: The Hilbert Space Setting 46
Exercises 57
Chapter 3 Operator Equations and Their Approximate
Solutions (II): Other Linear Operators 63
3.1 Bounded Linear Operator Equations and
Their Approximate Solvability 64
3.1.1 The approximate solvability problem 64
3.1.2 The perturbed operator equation 68
3.1.3 Operator equations on reflexive Banach space and
Hilbert space 69
xi
xii Contents
3.2 Densely Defined Linear Operators and Their Equations 73
3.2.1 Closable linear operator equation in a Banach space setting 74
3.2.2 Closed linear operator equation in a Hilbert space setting 76
3.2.3 Definite linear operator equation in a Hilbert space setting 80
3.2.4 K positive definite operator equation in a Hilbert space
setting 87
3.3 Stability of Approximation Schemes 94
3.4 Numerical Solutions of Boundary Value Problems 96
3.4.1 Ordinary differential equations 96
3.4.2 Partial differential equations 100
Exercises 105
Chapter 4 Topological Degrees and Fixed Point Equations .. .113
4.1 Topological Degrees of Continuous Operators in Euclidean Spaces. 114
4.1.1 Topological degrees of regular operators and their
integral representations 114
4.1.2 Basic properties of topological degrees 122
4.1.3 Topological degrees of continuous operators 124
4.2 Topological Degrees of Compact Fields 132
4.3 Generalized Topological Degrees of A Proper Operators 139
4.4 Fixed Point Theorems 144
4.4.1 Brouwer fixed point and open set invariant theorems 145
4.4.2 Schauder and Krasnosel skii fixed point theorems 147
4.4.3 Leray Schauder fixed point theorem 148
4.4.4 Boundary conditions and fixed point theorems 149
4.5 Approximate Solutions of Nonlinear Fixed Point Equations 151
4.5.1 Projective approximate solvability of fixed point equations 151
4.5.2 Projective solutions of nonlinear integral equations 154
Exercises 158
Chapter 5 Nonlinear Monotone Operator Equations
and Their Approximate Solutions 163
5.1 Continuity, Derivative, and Differential of Operators 164
5.1.1 Continuity of operators 164
5.1.2 Derivative and differential of operators 165
5.2 Monotone Operators from a Banach Space to Its Dual Space 174
5.2.1 Monotone operators 174
5.2.2 Monotonicity and semicontinuities 180
5.2.3 Strongly monotone operators 183
5.3 Approximate Solvability of Monotone Operator Equations 185
5.3.1 Monotone operator equations 185
5.3.2 The perturbation problem 192
5.3.3 Some remarks on the complex Banach space setting 194
Contents xiii
5.4 Solvability and Approximate Solutions of K Monotone
Operator Equations 195
5.4.1 K monotone operator equations 195
5.4.2 The perturbation problem 200
5.5 Application Examples: Numerical Solutions of Boundary
Value Problems 202
Exercises 221
Chapter 6 Operator Evolution Equations and
Their Projective Approximate Solutions 227
6.1 Preliminaries 228
6.1.1 Strongly and weakly measurable functions 228
6.1.2 Bochner integrals 229
6.1.3 Abstract functions on the Lp space 229
6.1.4 Smoothing operator and smooth approximation 231
6.1.5 Generalized derivatives of abstract functions and
the Hm space 233
6.2 Projective Solutions of First Order Evolution Equations 235
6.2.1 Initial boundary value problem of a linear parabolic
equation 235
6.2.2 Continuous time projection methods 237
6.2.3 Discrete time projection methods 252
6.2.4 Initial boundary value problems of nonlinear parabolic
equations 259
6.3 Projective Solutions of Second Order Evolution Equations 264
Exercises 280
References 285
Appendix A: Fundamental Functional Analysis 289
Appendix B: Introduction to Sobolev Spaces 317
Subject Index 339
|
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| id | DE-604.BV011754809 |
| illustrated | Illustrated |
| indexdate | 2024-12-20T10:18:06Z |
| institution | BVB |
| isbn | 9810230648 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-007932378 |
| oclc_num | 36498863 |
| open_access_boolean | |
| owner | DE-703 DE-706 DE-11 |
| owner_facet | DE-703 DE-706 DE-11 |
| physical | XIII, 343 S. graph. Darst. |
| publishDate | 1997 |
| publishDateSearch | 1997 |
| publishDateSort | 1997 |
| publisher | World Scientific |
| record_format | marc |
| series | Series in approximations and decompositions |
| series2 | Series in approximations and decompositions |
| spellingShingle | Chen, Mingjun Chen, Zhongying Chen, Guanrong 1948- Approximate solutions of operator equations Series in approximations and decompositions Approximation theory Operator equations Numerical solutions Operatorgleichung (DE-588)4043601-9 gnd Näherungsverfahren (DE-588)4206467-3 gnd |
| subject_GND | (DE-588)4043601-9 (DE-588)4206467-3 |
| title | Approximate solutions of operator equations |
| title_auth | Approximate solutions of operator equations |
| title_exact_search | Approximate solutions of operator equations |
| title_full | Approximate solutions of operator equations Mingjun Chen ; Zhongying Chen ; Guanrong Chen |
| title_fullStr | Approximate solutions of operator equations Mingjun Chen ; Zhongying Chen ; Guanrong Chen |
| title_full_unstemmed | Approximate solutions of operator equations Mingjun Chen ; Zhongying Chen ; Guanrong Chen |
| title_short | Approximate solutions of operator equations |
| title_sort | approximate solutions of operator equations |
| topic | Approximation theory Operator equations Numerical solutions Operatorgleichung (DE-588)4043601-9 gnd Näherungsverfahren (DE-588)4206467-3 gnd |
| topic_facet | Approximation theory Operator equations Numerical solutions Operatorgleichung Näherungsverfahren |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007932378&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV009569075 |
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