Approximate calculation of integrals:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
New York [u.a.]
Macmillan
1962
|
| Ausgabe: | 1. print. |
| Schriftenreihe: | ACM monograph series
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | X, 357 S. |
Internformat
MARC
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| 100 | 1 | |a Krylov, Vladimir I. |e Verfasser |4 aut | |
| 240 | 1 | 0 | |a Pribliz̆ennoe vyčislenie integralov |
| 245 | 1 | 0 | |a Approximate calculation of integrals |c Vladimir Ivanovich Krylov |
| 250 | |a 1. print. | ||
| 264 | 1 | |a New York [u.a.] |b Macmillan |c 1962 | |
| 300 | |a X, 357 S. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 0 | |a ACM monograph series | |
| 650 | 4 | |a Calcul approché | |
| 650 | 4 | |a Intégrales | |
| 650 | 4 | |a Approximation theory | |
| 650 | 4 | |a Integrals | |
| 650 | 0 | 7 | |a Numerische Integration |0 (DE-588)4172168-8 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Näherungsrechnung |0 (DE-588)4041115-1 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Approximation |0 (DE-588)4002498-2 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Integration |g Mathematik |0 (DE-588)4072852-3 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Integralrechnung |0 (DE-588)4027232-1 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Integral |0 (DE-588)4131477-3 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Integralrechnung |0 (DE-588)4027232-1 |D s |
| 689 | 0 | 1 | |a Näherungsrechnung |0 (DE-588)4041115-1 |D s |
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Datensatz im Suchindex
| _version_ | 1804118371011133440 |
|---|---|
| adam_text | CONTENTS
Preface v
Translator s Preface vi
PART ONE. PRELIMINARY INFORMATION
Chapter 1. Bernoulli Numbers and Bernoulli Polynomials 3
1.1. Bernoulli numbers 3
1.2. Bernoulli polynomials 6
1.3. Periodic functions related to Bernoulli polynomials 13
1.4. Expansion of an arbitrary function in Bernoulli
polynomials 15
Chapter 2. Orthogonal Polynomials
2.1. General theorems about orthogonal polynomials 18
2.2. Jacobi and Legendre polynomials 23
2.3. Chebyshev polynomials 26
2.4. Chebyshev Hermite polynomials 33
2.5. Chebyshev Laguerre polynomials 34
Chapter 3. Interpolation of Functions 37
3.1. Finite differences and divided differences 37
3.2. The interpolating polynomial and its remainder 42
3.3. Interpolation with multiple nodes 45
Chapter 4. Linear Nornted Spaces. Linear Operators 50
4.1. Linear normed spaces 50
4.2. Linear operators 54
4.3. Convergence of a sequence of linear operators 59
vii
viii Contents
PART TWO. APPROXIMATE CALCULATION OF DEFINITE
INTEGRALS
Chapter 5. Quadrature Sums and Problems Related to Them. The
Remainder in Approximate Quadrature 65
5.1. Quadrature sums 65
5.2. Remarks on the approximate integration of periodic
functions 73
5.3. The remainder in approximate quadrature and its
representation 74
Chapter 6. Interpolatory Quadratures 79
6.1. Interpolatory quadrature formulas and their remainder
terms 79
6.2. Newton Cotes formulas 82
6.3. Certain of the simplest Newton Cotes formulas 92
Chapter 7. Quadratures of the Highest Algebraic Degree of
Precision 100
7.1. General theorems 100
7.2. Constant weight function 107
7.3. Integrals of the form / * (b x)a(x a)Pf(x) dx and
a
their application to the calculation of multiple integrals 111
7.4. The integral J°° e~*2 f(x) dx 129
7.5. Integrals of the form J°° xae~xf(x) dx 130
Chapter 8. Quadrature Formulas with Least Estimate of the
Remainder 133
8.1. Minimization of the remainder of quadrature formulas 133
8.2. Minimization of the remainder in the class L9 134
8.3. Minimization of the remainder in the class Cr 149
8.4. The problem of minimizing the estimate of the remainder
for quadrature with fixed nodes 153
Chapter 9. Quadrature Formulas Containing Preassigned Nodes 160
9.1. General theorems 160
9.2. Formulas of special form 166
9.3. Remarks on integrals with weight functions that change
sign 174
Contents ix
Chapter 10. Quadrature Formulas with Equal Coefficients 179
10.1. Determining the nodes 179
10.2. Uniqueness of the quadrature formulas of the highest
algebraic degree of precision with equal coefficients 183
10.3. Integrals with a constant weight function 187
Chapter 11. Increasing the Precision of Quadrature Formulas 200
11.1. Two approaches to the problem 200
11.2. Weakening the singularity of the integrand 202
11.3. Euler s method for expanding the remainder 206
11.4. Increasing the precision when the integral representa¬
tion of the remainder contains a short principle sub
interval 229
Chapter 12. Convergence of the Quadrature Process 242
12.1. Introduction 242
12.2. Convergence of interpolatory quadrature formulas for
analytic functions 243
12.3. Convergence of the general quadrature process 264
PART THREE. APPROXIMATE CALCULATION OF INDEFINITE
INTEGRALS
Chapter 13. Introduction 277
13.1. Preliminary remarks 277
13.2. The error of the computation 281
13.3. Convergence and stability of the computational
process 288
Chapter 14. Integration of Functions Given in Tabular Form 298
14.1. One method for solving the problem 298
14.2. The remainder 302
Chapter 15. Calculation of Indefinite Integrals Using a Small
Number of Values of the Integrand 303
15.1. General aspects of the problem 303
15.2. Formulas of special form 309
Chapter 16. Methods Which Use Several Previous Values of the
Integral 320
16.1. Introduction 320
16.2. Conditions under which the highest degree of precision
is achieved 323
x Contents
16.3. The number of interpolating polynomials of the highest
degree of precision 326
16.4. The remainder of the interpolation and minimization of
its estimate 327
16.5. Conditions for which the coefficients a; are positive 329
16.6. Connection with the existence of a polynomial solution
to a certain differential equation 331
16.7. Some particular formulas 333
Appendix A. Gaussian Quadrature Formulas for Constant Weight
Function 337
Appendix B. Gaussian Hermite Quadrature Formulas 343
Appendix C. Gaussian Laguerre Quadrature Formulas 347
Index. 353
|
| any_adam_object | 1 |
| author | Krylov, Vladimir I. |
| author_facet | Krylov, Vladimir I. |
| author_role | aut |
| author_sort | Krylov, Vladimir I. |
| author_variant | v i k vi vik |
| building | Verbundindex |
| bvnumber | BV004159209 |
| callnumber-first | Q - Science |
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| callnumber-raw | QA311 |
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| callnumber-subject | QA - Mathematics |
| classification_rvk | SK 910 |
| ctrlnum | (OCoLC)809276 (DE-599)BVBBV004159209 |
| dewey-full | 517.31 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 517 - [Unassigned] |
| dewey-raw | 517.31 |
| dewey-search | 517.31 |
| dewey-sort | 3517.31 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| edition | 1. print. |
| format | Book |
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| id | DE-604.BV004159209 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T16:09:14Z |
| institution | BVB |
| language | English |
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| physical | X, 357 S. |
| publishDate | 1962 |
| publishDateSearch | 1962 |
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| publisher | Macmillan |
| record_format | marc |
| series2 | ACM monograph series |
| spelling | Krylov, Vladimir I. Verfasser aut Pribliz̆ennoe vyčislenie integralov Approximate calculation of integrals Vladimir Ivanovich Krylov 1. print. New York [u.a.] Macmillan 1962 X, 357 S. txt rdacontent n rdamedia nc rdacarrier ACM monograph series Calcul approché Intégrales Approximation theory Integrals Numerische Integration (DE-588)4172168-8 gnd rswk-swf Näherungsrechnung (DE-588)4041115-1 gnd rswk-swf Approximation (DE-588)4002498-2 gnd rswk-swf Integration Mathematik (DE-588)4072852-3 gnd rswk-swf Integralrechnung (DE-588)4027232-1 gnd rswk-swf Integral (DE-588)4131477-3 gnd rswk-swf Integralrechnung (DE-588)4027232-1 s Näherungsrechnung (DE-588)4041115-1 s DE-604 Numerische Integration (DE-588)4172168-8 s Integral (DE-588)4131477-3 s Approximation (DE-588)4002498-2 s Integration Mathematik (DE-588)4072852-3 s 1\p DE-604 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=002593874&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Krylov, Vladimir I. Approximate calculation of integrals Calcul approché Intégrales Approximation theory Integrals Numerische Integration (DE-588)4172168-8 gnd Näherungsrechnung (DE-588)4041115-1 gnd Approximation (DE-588)4002498-2 gnd Integration Mathematik (DE-588)4072852-3 gnd Integralrechnung (DE-588)4027232-1 gnd Integral (DE-588)4131477-3 gnd |
| subject_GND | (DE-588)4172168-8 (DE-588)4041115-1 (DE-588)4002498-2 (DE-588)4072852-3 (DE-588)4027232-1 (DE-588)4131477-3 |
| title | Approximate calculation of integrals |
| title_alt | Pribliz̆ennoe vyčislenie integralov |
| title_auth | Approximate calculation of integrals |
| title_exact_search | Approximate calculation of integrals |
| title_full | Approximate calculation of integrals Vladimir Ivanovich Krylov |
| title_fullStr | Approximate calculation of integrals Vladimir Ivanovich Krylov |
| title_full_unstemmed | Approximate calculation of integrals Vladimir Ivanovich Krylov |
| title_short | Approximate calculation of integrals |
| title_sort | approximate calculation of integrals |
| topic | Calcul approché Intégrales Approximation theory Integrals Numerische Integration (DE-588)4172168-8 gnd Näherungsrechnung (DE-588)4041115-1 gnd Approximation (DE-588)4002498-2 gnd Integration Mathematik (DE-588)4072852-3 gnd Integralrechnung (DE-588)4027232-1 gnd Integral (DE-588)4131477-3 gnd |
| topic_facet | Calcul approché Intégrales Approximation theory Integrals Numerische Integration Näherungsrechnung Approximation Integration Mathematik Integralrechnung Integral |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=002593874&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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