Numerical approximation to functions and data: based on a conference organized by the Institute of Mathematics and Its Applications, Canterbury, England, 1967
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| Format: | Book |
|---|---|
| Language: | English |
| Published: |
London
Athlone Press
1970
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| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | VIII, 177 S. Ill., graph. Darst. |
| ISBN: | 0485111098 |
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| 245 | 1 | 0 | |a Numerical approximation to functions and data |b based on a conference organized by the Institute of Mathematics and Its Applications, Canterbury, England, 1967 |c ed. by J. G. Hayes |
| 264 | 1 | |a London |b Athlone Press |c 1970 | |
| 300 | |a VIII, 177 S. |b Ill., graph. Darst. | ||
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Record in the Search Index
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| adam_text | CONTENTS
1 INTRODUCTION 1
L. POX, riMA, University of Oxford
2 GENERAL CONSIDERATIONS 4
C. W. CLENSHAW, fima, National Physical Laboratory, Teddington
1. Introduction, 4; 2. Choice of norm, 6; 3. Choice of approximating
function, 10; 4. Polynomials and splines, 12
3 THE POLYNOMIAL AND RATIONAL APPROXIMATION
OF A FUNCTION OF ONE VARIABLE 16
C. W. CLENSHAW, fima, National Physical Laboratory, Teddington
1. Introduction, 16; 2. Calculation of the minimax polynomial, 17;
3. Approximation in Chebyshev series, 19; 4. Use of the L% norm, 22;
5. Rational functions, 23; 6. Continued fractions, 24; 7. The Pade
table and the s algorithm, 25; 8. Conclusions, 26
4 THE APPROXIMATION OF A FUNCTION OF ONE
VARIABLE BY CUBIC SPLINES 28
A. R. CURTIS, fima, Atomic Energy Research Establishment, Harwell
1. Introduction, 28; 2. Description of the algorithm, 32; 3. Useful
results for constant knot spacing, 35; 4. Effect of change of interval, 36;
5. End of range conditions, 38; 6. Discussion, 40
5 CURVE FITTING BY POLYNOMIALS IN ONE
VARIABLE 43
J. Gr. HAYES, fima, National Physical Laboratory, Teddington
1. Introduction, 43; 2. Least squares, 43; 3. Orthogonal polynomials,
46; 4. Weighting, 48; 5. Constraints, 49; 6. Choice of degree of poly¬
nomial, 50; 7. Unsatisfactory fits, 53; 8. Examples, 54; 9. Conclud¬
ing remarks, 63
6 CURVE FITTING BY SPLINES IN ONE VARIABLE 65
M. J. D. POWELL, fima, Atomic Energy Research Establishment,
Harwell
1. Introduction, 65; 2. An outline of the algorithm, 67; 3. The need for
smoothing, 68; 4. The linear parameters of s(x), 70; 5. The test for
trends, 72; 6. The magnitude of the smoothing term, 74; 7. Numer¬
ical examples, 79
7 FITTING DATA IN MORE THAN ONE VARIABLE 84
J. G. HAYES, fima, National Physical Laboratory, Teddington
1. Introduction, 84; 2. General arrangement of data points, 87; 3.
Rectangular mesh of data points, 89; 4. Data on lines parallel to an axis:
rectangular boundary, 91; 5. Data on lines parallel to an axis: curved
boundary, 92; 6, Constraints, 94; 7. More than two independent vari¬
ables, 96; 8. Methods for surface interpolation, 96
viii CONTENTS
8 AN AUTOMATIC CURVE FITTING PACKAGE 98
J. A. PAYNE, Imperial Chemical Industries Ltd., Wilmslow
1. Introduction, 98; 2. Basic philosophy, 99; 3. Data scatter, 99; 4.
Data form, 102; 5. Single polynomial fit, 103; 6. Subdivision of data,
103; 7. Polynomial fitting in sections, 104
9 EXPERIENCE WITH CUBIC SPLINES IN THE
GRADUATION OF NEUTRON CROSS SECTION DATA 107
K. PAEKEE, Atomic Weapons Research Establishment, Aldermaston
10 METHODS OP GRADUATING HETEROGENEOUS DATA 111
J. B. PARKER, pima, Atomic Weapons Research Establishment,
Aldermaston
1. Introduction, 111; 2. Development of method, 112; 3. Examples, 114
11 COMPUTATIONAL EXPERIENCE IN SOLVING
LINEAR OPERATOR EQUATIONS USING THE
CHEBYSHEV NORM 115
I. BARRODALE1 and A. YOUNG2, fima, University of Liverpool
1. Introduction, 116; 2. Some linear operator equations, 116;
3. Integral equations, 116; 4. Ordinary differential equations, 125;
5. Integro differential equations, 132; 6. Partial differential equations,
133; 7. Conclusions, 142
12 OPTIMAL APPROXIMATION AND INTERPOLATION
IN NORMED SPACES 143
J. MEINGUET, Catholic University of Louvain, Belgium
1. Introduction, 143; 2. The characterization problem, 144; 3. A
method of solution and its geometric interpretation, 147; 4. Optimal
versus best error bounds, 150; 5. Lagrange interpolation and extrap¬
olation, 153
13 APPROXIMATION THEORY—YESTERDAY, TODAY
AND TOMORROW 158
P. J. DAVIS, Brown University, Rhode Island, USA
1. Introduction, 158; 2. Approximation theory a generation ago, 158;
3. Approximation theory today, 158; 4. What should approximators
be doing in the future?, 162; 5. The present position of numerical
analysis, 164
REFERENCES 167
INDEX 173
1 Now at the University of Victoria, B.C., Canada.
1 Now at the New University of Ulster, Northern Ireland.
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| spelling | Numerical approximation to functions and data based on a conference organized by the Institute of Mathematics and Its Applications, Canterbury, England, 1967 ed. by J. G. Hayes London Athlone Press 1970 VIII, 177 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Analyse numérique Analyse numérique ram Approximation, Théorie de l' ram Approximations (Mathématiques) Approximation theory Numerical analysis Computer (DE-588)4070083-5 gnd rswk-swf Approximationstheorie (DE-588)4120913-8 gnd rswk-swf Numerisches Verfahren (DE-588)4128130-5 gnd rswk-swf Funktion Mathematik (DE-588)4071510-3 gnd rswk-swf Approximation (DE-588)4002498-2 gnd rswk-swf (DE-588)1071861417 Konferenzschrift 1967 Canterbury gnd-content Approximation (DE-588)4002498-2 s Numerisches Verfahren (DE-588)4128130-5 s DE-604 Funktion Mathematik (DE-588)4071510-3 s Computer (DE-588)4070083-5 s Approximationstheorie (DE-588)4120913-8 s Hayes, James G. Sonstige oth Institute of Mathematics and Its Applications Sonstige (DE-588)1004217-9 oth HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=002640440&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Numerical approximation to functions and data based on a conference organized by the Institute of Mathematics and Its Applications, Canterbury, England, 1967 Analyse numérique Analyse numérique ram Approximation, Théorie de l' ram Approximations (Mathématiques) Approximation theory Numerical analysis Computer (DE-588)4070083-5 gnd Approximationstheorie (DE-588)4120913-8 gnd Numerisches Verfahren (DE-588)4128130-5 gnd Funktion Mathematik (DE-588)4071510-3 gnd Approximation (DE-588)4002498-2 gnd |
| subject_GND | (DE-588)4070083-5 (DE-588)4120913-8 (DE-588)4128130-5 (DE-588)4071510-3 (DE-588)4002498-2 (DE-588)1071861417 |
| title | Numerical approximation to functions and data based on a conference organized by the Institute of Mathematics and Its Applications, Canterbury, England, 1967 |
| title_auth | Numerical approximation to functions and data based on a conference organized by the Institute of Mathematics and Its Applications, Canterbury, England, 1967 |
| title_exact_search | Numerical approximation to functions and data based on a conference organized by the Institute of Mathematics and Its Applications, Canterbury, England, 1967 |
| title_full | Numerical approximation to functions and data based on a conference organized by the Institute of Mathematics and Its Applications, Canterbury, England, 1967 ed. by J. G. Hayes |
| title_fullStr | Numerical approximation to functions and data based on a conference organized by the Institute of Mathematics and Its Applications, Canterbury, England, 1967 ed. by J. G. Hayes |
| title_full_unstemmed | Numerical approximation to functions and data based on a conference organized by the Institute of Mathematics and Its Applications, Canterbury, England, 1967 ed. by J. G. Hayes |
| title_short | Numerical approximation to functions and data |
| title_sort | numerical approximation to functions and data based on a conference organized by the institute of mathematics and its applications canterbury england 1967 |
| title_sub | based on a conference organized by the Institute of Mathematics and Its Applications, Canterbury, England, 1967 |
| topic | Analyse numérique Analyse numérique ram Approximation, Théorie de l' ram Approximations (Mathématiques) Approximation theory Numerical analysis Computer (DE-588)4070083-5 gnd Approximationstheorie (DE-588)4120913-8 gnd Numerisches Verfahren (DE-588)4128130-5 gnd Funktion Mathematik (DE-588)4071510-3 gnd Approximation (DE-588)4002498-2 gnd |
| topic_facet | Analyse numérique Approximation, Théorie de l' Approximations (Mathématiques) Approximation theory Numerical analysis Computer Approximationstheorie Numerisches Verfahren Funktion Mathematik Approximation Konferenzschrift 1967 Canterbury |
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