The approximation of functions: 2 Nonlinear and multivariate theory
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| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Reading, Mass. [u.a.]
Addison-Wesley
1969
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| Series: | Addison-Wesley series in computer and information processing
|
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XIII, 334 S. graph. Darst. |
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Record in the Search Index
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| adam_text | Contents
Chapter Seven. Varisolvent Functions
7 1 Introduction 1
7 2 Varisolvent functions 3
7 3 Existence of best approximations 9
7 4 Basic theorems 9
7 5 Approximation on subsets 12
7 6 The limits of a Tchebycheff type theory—characterization . . 15
7 7 The problem with assumption s/ 17
7 8 The problem with assumption s/2 22
7 9 The limits of a Tchebycheff type theory—characterization and
existence 31
7 10 Areas of difficulty and unsolved problems 38
Chapter Eight. The Exponential Function and Related
Functions
8 1 Introduction 42
8 2 The exponential approximating function 42
8 3 Approximation from a curve of functions 46
8 4 The existence theorems for .^ approximation 48
8 5 Tchebycheft approximation and varisolvence 56
8 6 Concrete interpretations 63
8 7 Finite point sets and pseudo approximations 65
8 8 Computation 69
Chapter Nine. Rational Functions
9 1 Introduction 76
9 2 Existence theorems for the interval [0, 1] 77
9 3 Stability and existence for general rational functions .... 84
9 4 Characterization and uniqueness for general rational functions . 89
9 5 Polynomial rational functions 97
9 6 Computation 102
9 7 Computation—the Kernes algorithm 105
9 8 Computation—other methods 113
xi
xii CONTENTS
Chapter Ten. Spline Functions
10 1 Introduction 123
10—2 Spline functions and their basic properties 124
10 3 Existence theorems for nonlinear spline approximation . . . 129
10 4 Za approximation by splines 142
10 5 Tchebycheff approximation by splines 145
10 6 Splines and the approximation of linear functionals .... 154
10 7 Computational methods 159
Chapteb Eleven. Geometric Theory or Nonlinear
Approximation
11 1 Introduction 168
11 2 Approximation and projection 169
11—3 Unisolvent and locally unisolvent functions as manifolds . . . 171
11 4 Minkowski geometry 173
11—5 Curvature in Minkowski geometry 190
11 6 Motzkin sets and unique projections 198
11 7 Projections on submanifolds 201
11 8 Non manifold problems 212
11 9 Projections on objects 217
Chapteb Twelve. Multivariate Approximation
12 1 Introduction 224
12 2 Least squares and general orthonormal systems 225
12 3 Tensor products 227
12 4 Tchebycheff approximation—nonuniqueness 230
12 5 Tchebycheff approximation—characterization 232
12 6 Conditions for nonuniqueness 236
12 7 Strict approximation 239
12 8 The Polya algorithm 246
12 9 Computation 251
12 10 Orthogonalization 251
12 11 The one for one exchange algorithm 254
12 12 Critical point sets 258
Chapter Thirteen. Best Approximations and Interpolating
Functions
13 1 Introduction 260
13 2 Norms and regularity 263
13 3 Varisolvent approximating functions on an interval .... 267
13 4 Linear interpolating functions on an interval 273
13 5 Varisolvent approximations on a finite point set 278
13 6 Norm classes for finite point sets 279
13 7 Linear approximation and Lv nonas 283
CONTENTS Xiii
13 8 The Tchebychefl norm 290
13 9 Summary for £, norms and linear functions 291
13 10 Juxtapolynomiala 293
13 11 The Lawson algorithm 298
Bibliography 309
Index 329
|
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| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV002647178 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T15:47:52Z |
| institution | BVB |
| language | English |
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| physical | XIII, 334 S. graph. Darst. |
| publishDate | 1969 |
| publishDateSearch | 1969 |
| publishDateSort | 1969 |
| publisher | Addison-Wesley |
| record_format | marc |
| series2 | Addison-Wesley series in computer and information processing |
| spelling | Rice, John Rischard 1934- Verfasser (DE-588)123389240 aut The approximation of functions 2 Nonlinear and multivariate theory by John R. Rice Reading, Mass. [u.a.] Addison-Wesley 1969 XIII, 334 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Addison-Wesley series in computer and information processing (DE-604)BV002357830 2 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001698472&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Rice, John Rischard 1934- The approximation of functions |
| title | The approximation of functions |
| title_auth | The approximation of functions |
| title_exact_search | The approximation of functions |
| title_full | The approximation of functions 2 Nonlinear and multivariate theory by John R. Rice |
| title_fullStr | The approximation of functions 2 Nonlinear and multivariate theory by John R. Rice |
| title_full_unstemmed | The approximation of functions 2 Nonlinear and multivariate theory by John R. Rice |
| title_short | The approximation of functions |
| title_sort | the approximation of functions nonlinear and multivariate theory |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001698472&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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