Numerical analysis, algorithms and computation:
Gespeichert in:
| Hauptverfasser: | , , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Chichester u.a.
Horwood u.a.
1988
|
| Schriftenreihe: | Mathematics and its applications
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | VIII, 148 S. |
| ISBN: | 0853127514 0470212144 |
Internformat
MARC
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| 245 | 1 | 0 | |a Numerical analysis, algorithms and computation |c J. Murphy ; D. Ridout ; Bridgid McShane |
| 264 | 1 | |a Chichester u.a. |b Horwood u.a. |c 1988 | |
| 300 | |a VIII, 148 S. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 0 | |a Mathematics and its applications | |
| 650 | 0 | 7 | |a Numerische Mathematik |0 (DE-588)4042805-9 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Numerische Mathematik |0 (DE-588)4042805-9 |D s |
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| 700 | 1 | |a Ridout, Dennis |e Verfasser |4 aut | |
| 700 | 1 | |a MacShane, Brigid |e Verfasser |4 aut | |
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| 999 | |a oai:aleph.bib-bvb.de:BVB01-005481993 | ||
Datensatz im Suchindex
| _version_ | 1804122691304685568 |
|---|---|
| adam_text | Table of Contents
1 Introduction 1
1.1 Numerical/computational modelling 1
1.2 Number representation and error 1
1.3 Some prerequisites from Calculus 3
2 Iterative methods for non linear equations 7
2.1 Introduction 7
2.2 Simple iteration by algebraic transformation 8
2.3 Test for convergence 9
2.4 Rate of convergence 14
2.5 The bisection method 15
2.6 The Newton Raphson method for solving f(x) = 0 17
2.7 Equations with nearly equal roots 20
2.8 Real roots of polynomial equations 22
Exercises 2 26
3 Interpolation 30
3.1 Finite differences and difference operators 32
3.2 Interpolation formulae involving forward and backward diferences 40
3.3 Divided differences and Newton s divided difference formula 45
3.4 Central difference interpolation formulae 52
3.5 Choices of interpolation polynomial 59
Exercises 3 60
4 Numerical integration 63
4.1 Approximation of the integrand 65
4.2 Some well known integration formulae 66
4.2.1 The Trapezium rule 66
v
vi Tables of contents
4.2.2 Simpson s rule 70
4.3 Truncation error and classification of integration formulae 75
4.4 Higher order integration formulae 76
4.5 Choice of formula 77
4.6 Romberg integration 78
4.7 Closed and open integration formulae 82
Exercises 4 84
5 Numerical solution of ordinary differential equations 87
5.1 Multi step methods 89
5.1.1 Methods based on open integration 89
5.1.2 Methods based on closed integration 92
5.1.3 Starting methods 94
5.1.4 More general multi step methods 102
5.1.5 Accuracy of multi step formulae 103
5.1.6 Systems of equations and higher order equations 110
5.2 Single step methods 113
5.2.1 First order equations 113
5.2.2 Systems of equations and higher order equations 118
Exercises 5
6 Systems of linear equations 120
6.1 Direct methods 121
6.1.1 Triangular systems—forward and backward substitution 121
6.1.2 Gaussian elimination 122
6.1.3 Triangular factorization 128
6.2 Iterative techniques 135
6.2.1 Jacobi s method 135
6.2.2 The Gauss Siedel method 136
6.2.3 Successive over relaxation (S.O.R.) 137
6.2.4 Convergence 139
6.2.5 The iterative improvement procedure for removing round off
error 139
Exercises 6 141
Appendix 144
Homogeneous linear difference equations 144
Index 147
|
| any_adam_object | 1 |
| author | Murphy, John Ridout, Dennis MacShane, Brigid |
| author_facet | Murphy, John Ridout, Dennis MacShane, Brigid |
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| author_sort | Murphy, John |
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| bvnumber | BV008297983 |
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| ctrlnum | (OCoLC)256066710 (DE-599)BVBBV008297983 |
| dewey-full | 519.4 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 519 - Probabilities and applied mathematics |
| dewey-raw | 519.4 |
| dewey-search | 519.4 |
| dewey-sort | 3519.4 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV008297983 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T17:17:54Z |
| institution | BVB |
| isbn | 0853127514 0470212144 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-005481993 |
| oclc_num | 256066710 |
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| physical | VIII, 148 S. |
| publishDate | 1988 |
| publishDateSearch | 1988 |
| publishDateSort | 1988 |
| publisher | Horwood u.a. |
| record_format | marc |
| series2 | Mathematics and its applications |
| spelling | Murphy, John Verfasser aut Numerical analysis, algorithms and computation J. Murphy ; D. Ridout ; Bridgid McShane Chichester u.a. Horwood u.a. 1988 VIII, 148 S. txt rdacontent n rdamedia nc rdacarrier Mathematics and its applications Numerische Mathematik (DE-588)4042805-9 gnd rswk-swf Numerische Mathematik (DE-588)4042805-9 s DE-604 Ridout, Dennis Verfasser aut MacShane, Brigid Verfasser aut HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=005481993&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Murphy, John Ridout, Dennis MacShane, Brigid Numerical analysis, algorithms and computation Numerische Mathematik (DE-588)4042805-9 gnd |
| subject_GND | (DE-588)4042805-9 |
| title | Numerical analysis, algorithms and computation |
| title_auth | Numerical analysis, algorithms and computation |
| title_exact_search | Numerical analysis, algorithms and computation |
| title_full | Numerical analysis, algorithms and computation J. Murphy ; D. Ridout ; Bridgid McShane |
| title_fullStr | Numerical analysis, algorithms and computation J. Murphy ; D. Ridout ; Bridgid McShane |
| title_full_unstemmed | Numerical analysis, algorithms and computation J. Murphy ; D. Ridout ; Bridgid McShane |
| title_short | Numerical analysis, algorithms and computation |
| title_sort | numerical analysis algorithms and computation |
| topic | Numerische Mathematik (DE-588)4042805-9 gnd |
| topic_facet | Numerische Mathematik |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=005481993&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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