An introduction to numerical analysis:
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| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Cambridge
Cambridge Univ. Press
2003
|
| Edition: | 1. publ. |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | X, 433 S. Illustrationen |
| ISBN: | 0521810264 0521007941 |
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MARC
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| 100 | 1 | |a Süli, Endre |d 1956- |e Verfasser |0 (DE-588)1054382204 |4 aut | |
| 245 | 1 | 0 | |a An introduction to numerical analysis |c Endre Süli and David F. Mayers |
| 250 | |a 1. publ. | ||
| 264 | 1 | |a Cambridge |b Cambridge Univ. Press |c 2003 | |
| 300 | |a X, 433 S. |b Illustrationen | ||
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| 650 | 7 | |a Análise numérica |2 larpcal | |
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Record in the Search Index
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|---|---|
| adam_text | Contents
Preface
page
1
Solution of equations by iteration
1
1.1
Introduction
1
1.2
Simple iteration
2
1.3
Iterative solution of equations
17
1.4
Relaxation and Newton s method
19
1.5
The secant method
25
1.6
The bisection method
28
1.7
Global behaviour
29
1.8
Notes
32
Exercises
35
2
Solution of systems of linear equations
39
2.1
Introduction
39
2.2
Gaussian elimination
44
2.3
LU
48
2.4
Pivoting
52
2.5
Solution of systems of equations
55
2.6
Computational work
56
2.7
Norms and condition numbers
58
2.8
Hubert matrix
72
2.9
Least squares method
74
2.10
Notes
79
Exercises
82
3
Special matrices
87
3.1
Introduction
87
3.2
Symmetric positive definite matrices
87
3.3
Tridiagonal and band matrices
93
iv Contents
3.4
Monotone
98
3.5
Notes
101
Exercises
102
4
Simultaneous nonlinear equations
104
4.1
Introduction
104
4.2
Simultaneous iteration
106
4.3
Relaxation and Newton s method
116
4.4
Global convergence
123
4.5
Notes
124
Exercises
126
5
Eigenvalues and eigenvectors of a symmetric matrix
133
5.1
Introduction
133
5.2
The characteristic polynomial
137
5.3
Jacobi s method
137
5.4
The Gerschgorin theorems
145
5.5
Householder s method
150
5.6
Eigenvalues of a tridiagonal matrix
156
5.7
The QR algorithm
162
5.7.1
The QR factorisation revisited
162
5.7.2
The definition of the QR algorithm
164
5.8
Inverse iteration for the eigenvectors
166
5.9
The Rayleigh quotient
170
5.10
Perturbation analysis
172
5.11
Notes
174
Exercises
175
6
Polynomial interpolation
179
6.1
Introduction
179
6.2
Lagrange
180
6.3
Convergence
185
6.4
Hermite interpolation
187
6.5
Differentiation
191
6.6
Notes
194
Exercises
195
7
Numerical integration
200
7.1
Introduction
200
7.2
Newton-Cotes formulae
201
7.3
Error estimates
204
7.4
The
208
7.5
Composite formulae
209
Contents
V
7.6
The Euler-Maclaurin
211
7.7
Extrapolation
215
7.8
Notes
219
Exercises
220
8
Polynomial approximation in the oo-norm
224
8.1
Introduction
224
8.2
Normed linear spaces
224
8.3
Best approximation in the oo-norm
228
8.4
Chebyshev polynomials
241
8.5
Interpolation
244
8.6
Notes
247
Exercises
248
9
Approximation in the 2-norm
252
9.1
Introduction
252
9.2
Inner product spaces
253
9.3
Best approximation in the 2-norm
256
9.4
Orthogonal polynomials
259
9.5
Comparisons
270
9.6
Notes
272
Exercises
273
10
Numerical integration
277
10.1
Introduction
277
10.2
Construction of Gauss quadrature rules
277
10.3
Direct construction
280
10.4
Error estimation for Gauss quadrature
282
10.5
Composite Gauss formulae
285
10.6
Radau and Lobatto quadrature
287
10.7
Note
288
Exercises
288
11
Piecewise polynomial approximation
292
11.1
Introduction
292
11.2
Linear interpolating splines
293
11.3
Basis functions for the linear spline
297
11.4
Cubic splines
298
11.5
Hermite cubic splines
300
11.6
Basis functions for cubic splines
302
11.7
Notes
306
Exercises
307
vi
12
310
12.1
310
12.2
317
12.3
321
12.4
324
12.5
325
12.6
329
12.7
331
12.8
337
12.9
340
12.10
341
12.11
343
12.12
349
12.13
353
Exercises
355
13
361
13.1
361
13.2
361
13.3
364
13.4
367
13.5
370
13.6
373
13.7
375
13.8
380
Exercises
381
14
385
14.1
385
14.2
388
14.3
391
14.4
397
14.5
403
14.6
412
Exercises
414
Appendix A An overview of results from real analysis
419
Appendix
423
Bibliography
424
Index
429
|
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| discipline | Mathematik |
| edition | 1. publ. |
| format | Book |
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| illustrated | Illustrated |
| indexdate | 2024-07-09T19:10:26Z |
| institution | BVB |
| isbn | 0521810264 0521007941 |
| language | English |
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| spelling | Süli, Endre 1956- Verfasser (DE-588)1054382204 aut An introduction to numerical analysis Endre Süli and David F. Mayers 1. publ. Cambridge Cambridge Univ. Press 2003 X, 433 S. Illustrationen txt rdacontent n rdamedia nc rdacarrier Análise numérica larpcal Numerieke wiskunde gtt Numerical analysis Numerische Mathematik (DE-588)4042805-9 gnd rswk-swf Numerische Mathematik (DE-588)4042805-9 s DE-604 Mayers, David F. Verfasser (DE-588)1054382565 aut Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=010162265&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Süli, Endre 1956- Mayers, David F. An introduction to numerical analysis Análise numérica larpcal Numerieke wiskunde gtt Numerical analysis Numerische Mathematik (DE-588)4042805-9 gnd |
| subject_GND | (DE-588)4042805-9 |
| title | An introduction to numerical analysis |
| title_auth | An introduction to numerical analysis |
| title_exact_search | An introduction to numerical analysis |
| title_full | An introduction to numerical analysis Endre Süli and David F. Mayers |
| title_fullStr | An introduction to numerical analysis Endre Süli and David F. Mayers |
| title_full_unstemmed | An introduction to numerical analysis Endre Süli and David F. Mayers |
| title_short | An introduction to numerical analysis |
| title_sort | an introduction to numerical analysis |
| topic | Análise numérica larpcal Numerieke wiskunde gtt Numerical analysis Numerische Mathematik (DE-588)4042805-9 gnd |
| topic_facet | Análise numérica Numerieke wiskunde Numerical analysis Numerische Mathematik |
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