A first course in numerical methods:
Gespeichert in:
| Beteiligte Personen: | , |
|---|---|
| Format: | Buch |
| Sprache: | Englisch |
| Veröffentlicht: |
Philadelphia
siam, Society for Industrial and Applied Mathematics
[2011]
|
| Schriftenreihe: | Computational science and engineering series
7 |
| Schlagwörter: | |
| Links: | http://www.loc.gov/catdir/enhancements/fy1111/2011007041-b.html http://www.loc.gov/catdir/enhancements/fy1111/2011007041-d.html http://www.loc.gov/catdir/enhancements/fy1111/2011007041-t.html http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=024505654&sequence=000003&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=024505654&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA |
| Umfang: | xxii, 552 Seiten Illustrationen |
| ISBN: | 9780898719970 |
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| 245 | 1 | 0 | |a A first course in numerical methods |c Uri M. Ascher, Chen Greif, The University of British Columbia, Vancouver, British Columbia, Canada |
| 264 | 1 | |a Philadelphia |b siam, Society for Industrial and Applied Mathematics |c [2011] | |
| 300 | |a xxii, 552 Seiten |b Illustrationen | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Computational science and engineering series |v 7 | |
| 650 | 4 | |a Datenverarbeitung | |
| 650 | 4 | |a Numerical calculations |x Data processing | |
| 650 | 4 | |a Numerical analysis | |
| 650 | 4 | |a Algorithms | |
| 650 | 0 | 7 | |a Numerische Mathematik |0 (DE-588)4042805-9 |2 gnd |9 rswk-swf |
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| 830 | 0 | |a Computational science and engineering series |v 7 |w (DE-604)BV022382702 |9 7 | |
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Datensatz im Suchindex
| DE-BY-TUM_call_number | 0102 MAT 650f 2011 A 8728 0104 MAT 650f 2011 A 8728 0303 MAT 650f 2011 L 1356 |
|---|---|
| DE-BY-TUM_katkey | 1786223 |
| DE-BY-TUM_location | 01 03 |
| DE-BY-TUM_media_number | 040010815015 040071380131 040008860571 040008860935 040071380197 040071380186 040071380175 040071380164 040071380153 |
| _version_ | 1821933599799115776 |
| adam_text | Contents
List of Figures
xi
List of Tables
xix
Preface
xxi
1
Numerical Algorithms
1
1.1
Scientific computing
............................... 1
1.2
Numerical algorithms and errors
........................ 3
1.3
Algorithm properties
............................... 9
1.4
Exercises
..................................... 14
1.5
Additional notes
................................. 15
2
Roundoff Errors
17
2.1
The essentials
.................................. 17
2.2
Floating point systems
.............................. 21
2.3
Roundoff error accumulation
.......................... 26
2.4
The IEEE standard
................................ 29
2.5
Exercises
..................................... 32
2.6
Additional notes
................................. 36
3
Nonlinear Equations in One Variable
39
3.1
Solving nonlinear equations
........................... 39
3.2
Bisection method
................................ 43
3.3
Fixed point iteration
............................... 45
3.4
Newton s method and variants
.......................... 50
3.5
Minimizing a function in one variable
...................... 55
3.6
Exercises
..................................... 58
3.7
Additional notes
................................. 64
4
Linear Algebra Background
65
4.1
Review of basic concepts
............................ 65
4.2
Vector and matrix norms
............................. 73
4.3
Special classes of matrices
............................ 78
4.4
Singular values
.................................. 80
4.5
Examples
..................................... 83
4.6
Exercises
..................................... 89
4.7
Additional notes
................................. 92
vii
v¡ ¡¡
Contents
5
Linear Systems: Direct Methods
93
5.1
Gaussian elimination and backward substitution
................ 94
5.2
LU
decomposition
................................ 100
5.3
Pivoting strategies
................................ 105
5.4
Efficient implementation
............................. 110
5.5
The Cholesky decomposition
.......................... 114
5.6
Sparse matrices
................................. 117
5.7
Permutations and ordering strategies
...................... 122
5.8
Estimating errors and the condition number
................... 127
5.9
Exercises
..................................... 133
5.10
Additional notes
................................. 139
6
Linear Least Squares Problems
141
6.1
Least squares and the normal equations
..................... 141
6.2
Orthogonal transformations and QR
....................... 151
6.3
Householder transformations and Gram-Schmidt orthogonalization
...... 157
6.4
Exercises
..................................... 163
6.5
Additional notes
................................. 166
7
Linear Systems: Iterative Methods
167
7.1
The need for iterative methods
......................... 167
7.2
Stationary iteration and relaxation methods
................... 173
7.3
Convergence of stationary methods
....................... 179
7.4
Conjugate gradient method
........................... 182
7.5
*Krylov subspace methods
........................... 191
7.6
*Multigrid methods
............................... 204
7.7
Exercises
..................................... 210
7.8
Additional notes
................................. 218
8
Eigenvalues and Singular Values
219
8.1
The power method and variants
......................... 219
8.2
Singular value decomposition
.......................... 229
8.3
General methods for computing eigenvalues and singular values
........ 236
8.4
Exercises
..................................... 245
8.5
Additional notes
................................. 249
9
Nonlinear Systems and Optimization
251
9.1
Newton s method for nonlinear systems
..................... 251
9.2
Unconstrained optimization
........................... 258
9.3
♦Constrained optimization
............................ 271
9.4
Exercises
..................................... 286
9.5
Additional notes
................................. 293
10
Polynomial Interpolation
295
10.1
General approximation and interpolation
.................... 295
10.2
Monomial interpolation
............................. 298
10.3 Lagrange
interpolation
.............................. 302
10.4
Divided differences and Newton s form
..................... 306
10.5
The error in polynomial interpolation
...................... 313
10.6
Chebyshev interpolation
............................. 316
10.7
Interpolating also derivative values
....................... 319
Contents ix
10.8
Exercises
..................................... 323
10.9
Additional notes
................................. 330
11
Piecewise Polynomial Interpolation
331
11.1
The case for piecewise polynomial interpolation
................ 331
11.2
Broken line and piecewise Hermite interpolation
................ 333
11.3
Cubic spline interpolation
............................ 337
11.4
Hat functions and B-splines
........................... 344
11.5
Parametric curves
................................ 349
11.6
♦Multidimensional interpolation
........................ 353
11.7
Exercises
..................................... 359
11.8
Additional notes
................................. 363
12
Best Approximation
365
12.1
Continuous least squares approximation
.................... 366
12.2
Orthogonal basis functions
........................... 370
12.3
Weighted least squares
.............................. 373
12.4
Chebyshev polynomials
............................. 377
12.5
Exercises
..................................... 379
12.6
Additional notes
................................. 382
13
Fourier Transform
383
13.1
The Fourier transform
.............................. 383
13.2
Discrete Fourier transform and trigonometric interpolation
........... 388
13.3
Fast Fourier transform
.............................. 396
13.4
Exercises
..................................... 405
13.5
Additional notes
................................. 406
14
Numerical Differentiation
409
14.1
Deriving formulas using Taylor series
...................... 409
14.2
Richardson extrapolation
............................ 413
14.3
Deriving formulas using
Lagrange
polynomial interpolation
.......... 415
14.4
Roundoff and data errors in numerical differentiation
............. 420
14.5
♦Differentiation matrices and global derivative approximation
......... 426
14.6
Exercises
..................................... 434
14.7
Additional notes
................................. 438
15
Numerical Integration
441
15.1
Basic quadrature algorithms
........................... 442
15.2
Composite numerical integration
........................ 446
15.3
Gaussian quadrature
............................... 454
15.4
Adaptive quadrature
............................... 462
15.5
Romberg integration
............................... 469
15.6
♦Multidimensional integration
.......................... 472
15.7
Exercises
..................................... 475
15.8
Additional notes
................................. 479
16
Differential Equations
481
16.1
Initial value ordinary differential equations
................... 481
16.2
Euler s method
.................................. 485
16.3
Runge-Kutta methods
.............................. 493
χ
Contents
16.4 Multistep
methods
................................ 500
16.5 Absolute
stability and stiffness
......................... 507
16.6
Error control and estimation
........................... 515
16.7
*Boundary value ODEs
............................. 520
16.8
*Partial differential equations
.......................... 524
16.9
Exercises
..................................... 531
16.10
Additional notes
................................. 537
Bibliography
539
Index
543
A First Course in Numerical Methods is designed for students and researchers who
seek practical knowledge of modern techniques in scientific computing. Avoiding
encyclopedic and heavily theoretical exposition, the book gives an in-depth treatment
of fundamental issues and methods, offers reasons behind the success and failure of
numerical software, and provides fresh and easy-to-follow approaches and techniques.
The authors take an algorithmic approach, focusing on techniques that have a high level
of applicability to engineering, computer science, and industrial mathematics. They
•
focus on current methods, issues, and software while providing a comprehensive
theoretical foundation, enabling those who need to apply the techniques to
successfully design solutions to
nonstandard
problems;
•
illustrate algorithms using the programming environment of
MATLAB®,
with the
expectation that the reader will gradually become proficient while learning
the material covered in the book; and
•
provide a variety of exercises within each chapter and review questions aimed
at self-testing.
A First Course in Numerical Methods is aimed at undergraduate and beginning
graduate students. It may also be appropriate for researchers whose main area of
expertise is not scientific computing and who are interested in learning the basic
concepts of the field.
Uri
M.
Ascher
is Professor of Computer Science at the University
of British Columbia in Vancouver, Canada. He has previously
co-authored three other SIAM books as well as many research papers
in the general area of numerical methods and their applications.
He is a SIAM Fellow and a recipient of the CAIMS Research Prize.
Chen
Greif
is Associate Professor of Computer Science at the
University of British Columbia in Vancouver, Canada. His research
interests are in the field of scientific computing, with specialization
in numerical linear algebra. He is currently an associate editor for
the SIAM Journal on Scientific Computing.
For more information about SIAM books, journals,
conferences, memberships, or activities, contact:
Society for Industrial and Applied Mathematics
3600
Market Street, 6th Floor
Philadelphia, PA
19104-2688
USA
+ 1-215-382-9800 ·
Fax:
+1-215-386-7999
siam@siam.org
*
www.siam.org
RKCSOOr
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| id | DE-604.BV039656104 |
| illustrated | Illustrated |
| indexdate | 2024-12-20T15:59:31Z |
| institution | BVB |
| isbn | 9780898719970 |
| language | English |
| lccn | 2011007041 |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-024505654 |
| oclc_num | 743645630 |
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| physical | xxii, 552 Seiten Illustrationen |
| publishDate | 2011 |
| publishDateSearch | 2011 |
| publishDateSort | 2011 |
| publisher | siam, Society for Industrial and Applied Mathematics |
| record_format | marc |
| series | Computational science and engineering series |
| series2 | Computational science and engineering series |
| spellingShingle | Ascher, Uri M. 1946- Greif, Chen 1965- A first course in numerical methods Computational science and engineering series Datenverarbeitung Numerical calculations Data processing Numerical analysis Algorithms Numerische Mathematik (DE-588)4042805-9 gnd Algorithmus (DE-588)4001183-5 gnd |
| subject_GND | (DE-588)4042805-9 (DE-588)4001183-5 |
| title | A first course in numerical methods |
| title_auth | A first course in numerical methods |
| title_exact_search | A first course in numerical methods |
| title_full | A first course in numerical methods Uri M. Ascher, Chen Greif, The University of British Columbia, Vancouver, British Columbia, Canada |
| title_fullStr | A first course in numerical methods Uri M. Ascher, Chen Greif, The University of British Columbia, Vancouver, British Columbia, Canada |
| title_full_unstemmed | A first course in numerical methods Uri M. Ascher, Chen Greif, The University of British Columbia, Vancouver, British Columbia, Canada |
| title_short | A first course in numerical methods |
| title_sort | a first course in numerical methods |
| topic | Datenverarbeitung Numerical calculations Data processing Numerical analysis Algorithms Numerische Mathematik (DE-588)4042805-9 gnd Algorithmus (DE-588)4001183-5 gnd |
| topic_facet | Datenverarbeitung Numerical calculations Data processing Numerical analysis Algorithms Numerische Mathematik Algorithmus |
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Teilbibliothek Mathematik & Informatik
| Signatur: |
0102 MAT 650f 2011 A 8728
Lageplan 0104 MAT 650f 2011 A 8728 Lageplan |
|---|---|
| Exemplar 1 | Ausleihbar Am Standort |
| Exemplar 1 | Nicht ausleihbar Am Standort |
Teilbibliothek Chemie, Lehrbuchsammlung
| Signatur: |
0303 MAT 650f 2011 L 1356
Lageplan |
|---|---|
| Exemplar 1 | Ausleihbar Am Standort |
| Exemplar 2 | Ausleihbar Am Standort |
| Exemplar 3 | Ausleihbar Am Standort |
| Exemplar 4 | Ausleihbar Am Standort |
| Exemplar 5 | Ausleihbar Am Standort |
| Exemplar 6 | Ausleihbar Am Standort |
| Exemplar 7 | Ausleihbar Am Standort |