Numerical analysis:
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| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Princeton [u.a.]
Princeton Univ. Press
2011
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| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XIV, 325 S. graph. Darst. |
| ISBN: | 9780691146867 0691146861 |
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MARC
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| 100 | 1 | |a Scott, L. Ridgway |e Verfasser |0 (DE-588)124153356 |4 aut | |
| 245 | 1 | 0 | |a Numerical analysis |c L. Ridgway Scott |
| 264 | 1 | |a Princeton [u.a.] |b Princeton Univ. Press |c 2011 | |
| 300 | |a XIV, 325 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
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Record in the Search Index
| _version_ | 1804147952632987648 |
|---|---|
| adam_text | Contents
Preface
xi
1
2
5
6
8
9
11
13
15
16
20
25
26
27
27
30
35
36
38
42
44
47
47
50
Chapter
4.
Direct Solvers 51
4.1
Direct factorization
51
4.2
Caution about factorization
56
4.3
Banded matrices
58
4.4
More reading
60
4.5
Exercises
60
4.6
Solutions 63
Chapter
1.
Numerical Algorithms
1.1
Finding roots
1.2
Analyzing Heron s algorithm
1.3
Where to start
1.4
An unstable algorithm
1.5
General roots: effects of floating-point
1.6
Exercises
1.7
Solutions
Chapter
2.
Nonlinear Equations
2.1
Fixed-point iteration
2.2
Particular methods
2.3
Complex roots
2.4
Error propagation
2.5
More reading
2.6
Exercises
2.7
Solutions
Chapter
3.
Linear Systems
3.1
Gaussian elimination
3.2
Factorization
3.3
Triangular matrices
3.4
Pivoting
3.5
More reading
3.6
Exercises
3.7
Solutions
v¡¡¡
CONTENTS
Chapter
5.
Vector Spaces 65
5.1
Normed vector spaces
66
5.2
Proving the triangle inequality
69
5.3
Relations between norms
71
5.4
Inner-product spaces
72
5.5
More reading
76
5.6
Exercises
77
5.7
Solutions
79
Chapter
6.
Operators
81
6.1
Operators
82
6.2 Schur
decomposition
84
6.3
Convergent matrices
89
6.4
Powers of matrices
89
6.5
Exercises
92
6.6
Solutions
95
Chapter
7.
Nonlinear Systems
97
7.1
Functional iteration for systems
98
7.2
Newton s method
103
7.3
Limiting behavior of Newton s method
108
7.4
Mixing solvers
110
7.5
More reading 111
7.6
Exercises 111
7.7
Solutions
114
Chapter
8.
Iterative Methods
115
8.1
Stationary iterative methods
116
8.2
General splittings
117
8.3
Necessary conditions for convergence
123
8.4
More reading
128
8.5
Exercises
128
8.6
Solutions
131
Chapter
9.
Conjugate Gradients
133
9.1
Minimization methods
133
9.2
Conjugate Gradient iteration
137
9.3
Optimal approximation of
CG 141
9.4
Comparing iterative solvers
147
9.5
More reading
147
9.6
Exercises
148
9.7
Solutions
149
CONTENTS ¡x
Chapter
10.
Polynomial Interpolation
151
10.1
Local approximation: Taylor s theorem
151
10.2
Distributed approximation: interpolation
152
10.3
Norms in infinite-dimensional spaces
157
10.4
More reading
160
10.5
Exercises
160
10.6
Solutions
163
Chapter
11.
Chebyshev and Hermite Interpolation
167
11.1
Error term
ω
167
11.2
Chebyshev basis functions
170
11.3
Lebesgue function
171
11.4
Generalized interpolation
173
11.5
More reading
177
11.6
Exercises
178
11.7
Solutions
180
Chapter
12.
Approximation Theory
183
12.1
Best approximation by polynomials
183
12.2
Weierstrass
and Bernstein
187
12.3
Least squares 191
12.4
Piecewise polynomial approximation 1 3
12.5
Adaptive approximation
195
12.6
More reading l96
12.7
Exercises
ł96
12.8
Solutions 199
Chapter
13.
Numerical Quadrature 203
13.1
Interpolatory
quadrature
^3
13.2
Peano kernel theorem 209
13.3
Gregorie-Euler-Maclaurin formulas 212
13.4
Other quadrature rules
219
13.5
More reading
13.6
Exercises 221
13.7
Solutions 224
Chapter
14.
Eigenvalue Problems 22-
14.1
Eigenvalue examples
14.2
Gershgorin s theorem
14.3
Solving separately 232
14.4
How not to
eigen
2
14.5
Reduction to
Hessenberg form
234
14.6
More reading 237
14.7
Exercises 238
14.8
Solutions 24°
x
CONTENTS
Chapter
15.
Eigenvalue Algorithms
241
15.1
Power method
241
15.2
Inverse iteration
250
15.3
Singular value decomposition
252
15.4
Comparing factorizations
253
15.5
More reading
254
15.6
Exercises
254
15.7
Solutions
256
Chapter
16.
Ordinary Differential Equations
257
16.1
Basic theory of ODEs
257
16.2
Existence and uniqueness of solutions
258
16.3
Basic discretization methods
262
16.4
Convergence of discretization methods
266
16.5
More reading
269
16.6
Exercises
269
16.7
Solutions
271
Chapter
17.
Higher-order ODE Discretization Methods
275
17.1
Higher-order discretization
276
17.2
Convergence conditions
281
17.3
Backward differentiation formulas
287
17.4
More reading
288
17.5
Exercises
289
17.6
Solutions
291
Chapter
18.
Floating Point
293
18.1
Floating-point arithmetic
293
18.2
Errors in solving systems
301
18.3
More reading
305
18.4
Exercises
305
18.5
Solutions
308
Chapter
19.
Notation
309
Bibliography
311
Index
323
|
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| indexdate | 2024-07-09T23:59:25Z |
| institution | BVB |
| isbn | 9780691146867 0691146861 |
| language | English |
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| physical | XIV, 325 S. graph. Darst. |
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| publisher | Princeton Univ. Press |
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| spelling | Scott, L. Ridgway Verfasser (DE-588)124153356 aut Numerical analysis L. Ridgway Scott Princeton [u.a.] Princeton Univ. Press 2011 XIV, 325 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Numerische Mathematik (DE-588)4042805-9 gnd rswk-swf (DE-588)4123623-3 Lehrbuch gnd-content Numerische Mathematik (DE-588)4042805-9 s DE-604 Digitalisierung UB Bamberg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=024140162&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Scott, L. Ridgway Numerical analysis Numerische Mathematik (DE-588)4042805-9 gnd |
| subject_GND | (DE-588)4042805-9 (DE-588)4123623-3 |
| title | Numerical analysis |
| title_auth | Numerical analysis |
| title_exact_search | Numerical analysis |
| title_full | Numerical analysis L. Ridgway Scott |
| title_fullStr | Numerical analysis L. Ridgway Scott |
| title_full_unstemmed | Numerical analysis L. Ridgway Scott |
| title_short | Numerical analysis |
| title_sort | numerical analysis |
| topic | Numerische Mathematik (DE-588)4042805-9 gnd |
| topic_facet | Numerische Mathematik Lehrbuch |
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