Essentials of scientific computing: numerical methods for science and engineering
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Chichester, UK
Horwood Pub.
2008
|
| Edition: | 1. publ. |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | 218 S. ill., graph. Darst. |
| ISBN: | 9781904275329 9781588902436 |
Staff View
MARC
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| 100 | 1 | |a Zalizniak, Victor |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Essentials of scientific computing |b numerical methods for science and engineering |c Victor Zalizniak |
| 250 | |a 1. publ. | ||
| 264 | 1 | |a Chichester, UK |b Horwood Pub. |c 2008 | |
| 300 | |a 218 S. |b ill., graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
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| 338 | |b nc |2 rdacarrier | ||
| 650 | 4 | |a Datenverarbeitung | |
| 650 | 4 | |a Informatik | |
| 650 | 4 | |a Mathematik | |
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| 650 | 4 | |a Numerical analysis |x Data processing | |
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Record in the Search Index
| _version_ | 1804138836531347456 |
|---|---|
| adam_text | TABLE
OF
CONTENTS
CHAPTER
1
Errors in computer arithmetic operations l
CHAPTER
2
Solving equations of the form
Дж)=0
5
2.1
The bisection method
7
2.2
Calculation of roots with the use of iterative functions
8
2.2.1
One-point iterative processes
11
2.2.2
Multi-point iterative processes
16
2.2.3
One-point iterative processes with memory
18
2.3
Concluding remarks
19
CHAPTER
3
Solving systems of linear equations
2
1
3.1
Linear algebra background
22
3.2
Systems of linear equations
24
3.3
Types of matrices that arise from applications and
25
analysis
3.3.1
Sparse matrices
25
3.3.2
Band matrices
25
3.3.3
Symmetric positive definite matrices
26
3.3.4
Triangular matrices
26
3.3.5
Orthogonal matrices
27
3.3.6
Reducible matrices
27
3.3.7
Matrices with diagonal dominance
27
3.4
Error sources
27
3.5
Condition number
28
3.6
Direct methods
30
3.6.1
Basic principles of direct methods
30
3.6.2
Error estimation for linear systems
33
3.6.3
Concluding remarks
33
3.7
Iterative methods
34
3.7.1
Basic principles of iterative methods
34
3.7.2
Jacobi method
36
3.7.3
Gauss-Seidel method
37
3.7.4
Method of relaxation
39
3.7.5
Variational iterative methods
42
3.8
Comparative efficacy of direct and iterative methods
45
CHAPTER
4
Computational eigenvalue problems
47
4.1
Basic facts concerning eigenvalue problems
48
4.2
Localization of eigenvalues
49
4.3
Power method
49
4.4
Inverse iteration
51
4.5
Iteration with a shift of origin
53
4.6
The QR method
55
4.7
Concluding remarks
58
CHAPTER
5
Solving systems of nonlinear equations
59
5.1
Fixed-point iteration
60
5.2
Newton s method
65
5.3
Method with cubic convergence
68
5.4
Modification of Newton s method
69
5.5
Making the Newton-based techniques more reliable
71
CHAPTER
6
Numerical integration
74
6.1
Simple quadrature formulae
75
6.2
Computation of integrals with prescribed accuracy
80
6.3
Integration formulae of Gaussian type
84
6.4
Dealing with improper integrals
88
6.4.1
Integration over an infinite interval
88
6.4.2
Singular integrands
89
6.5
Multidimensional integration
90
CHAPTER
7
Introduction to finite difference schemes
97
for ordinary differential equations
7.1
Elementary example of a finite difference scheme
98
7.2
Approximation and stability
100
7.2.1
Approximation of differential equations by the difference scheme
101
7.2.2
Replacement of derivatives by difference expressions
105
7.2.3
Definition of stability of difference schemes
107
7.2.4
Convergence as a consequence of approximation and stability
107
7.3
Numerical solution of initial-value problems
108
7.3.1
Stability of difference schemes for linear problems
109
7.3.2
Runge-Kutta methods
112
7.3.3
Adams type methods
115
7.3.4
Method for studying stability of difference schemes for nonlinear
119
problems
7.3.5
Systems of differential equations
121
7.3.6
Methods for stiff differential equations
124
7.4
Numerical solution of boundary-value problems
128
7.4.1
The shooting method
128
7.4.2
Conversion of difference schemes to systems of equations
130
7.4.3
Method of successive approximations
132
7.4.4
Method of time development
134
7.4.5
Accurate approximation of boundary conditions when derivatives
138
are specified at boundary points
7.5
Error estimation and control
140
CHAPTER
8
Interpolation and Approximation
144
8.1
Interpolation
144
8.1.1
Polynomial interpolation
145
8.1.2
Trigonometric interpolation
148
8.1.3
Interpolation by splines
151
8.1.4
Two-dimensional interpolation
154
8.2 Approximation
of functions and data representation
156
8.2.1
Least-squares approximation
156
8.2.2
Approximation by orthogonal functions
161
8.2.3
Approximation by interpolating polynomials
166
CHAPTER
9
Programming in
MATLAB
169
9.1
Numbers, variables and special characters
170
9.2
Arithmetic and logical expressions
171
9.3
Conditional execution
171
9.4
Loops
173
9.5
Arrays
174
9.6
Functions
176
9.7
Input and output
178
9.8
Visualization
180
APPENDIX A Integration formulae of Gaussian type
183
APPENDIX
В
Transformations of integration domains
192
APPENDIX
С
Stability regions for Runge-Kutta and
194
Adams schemes
APPENDIX
D
A brief survey of available software
195
LAPACK library for problems in numerical linear algebra
195
IMSL mathematics and statistics libraries
198
Numerical Algorithms Group (NAG) numerical libraries
203
MATLAB
numerical functions
210
BIBLIOGRAPHY
212
INDEX
215
|
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| discipline | Informatik Mathematik |
| edition | 1. publ. |
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| illustrated | Illustrated |
| indexdate | 2024-07-09T21:34:31Z |
| institution | BVB |
| isbn | 9781904275329 9781588902436 |
| language | English |
| lccn | 2008411215 |
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| physical | 218 S. ill., graph. Darst. |
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| spelling | Zalizniak, Victor Verfasser aut Essentials of scientific computing numerical methods for science and engineering Victor Zalizniak 1. publ. Chichester, UK Horwood Pub. 2008 218 S. ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Datenverarbeitung Informatik Mathematik Computer science Mathematics Numerical analysis Data processing Numerische Mathematik (DE-588)4042805-9 gnd rswk-swf Numerische Mathematik (DE-588)4042805-9 s DE-604 Digitalisierung UB Bayreuth application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017326815&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Zalizniak, Victor Essentials of scientific computing numerical methods for science and engineering Datenverarbeitung Informatik Mathematik Computer science Mathematics Numerical analysis Data processing Numerische Mathematik (DE-588)4042805-9 gnd |
| subject_GND | (DE-588)4042805-9 |
| title | Essentials of scientific computing numerical methods for science and engineering |
| title_auth | Essentials of scientific computing numerical methods for science and engineering |
| title_exact_search | Essentials of scientific computing numerical methods for science and engineering |
| title_full | Essentials of scientific computing numerical methods for science and engineering Victor Zalizniak |
| title_fullStr | Essentials of scientific computing numerical methods for science and engineering Victor Zalizniak |
| title_full_unstemmed | Essentials of scientific computing numerical methods for science and engineering Victor Zalizniak |
| title_short | Essentials of scientific computing |
| title_sort | essentials of scientific computing numerical methods for science and engineering |
| title_sub | numerical methods for science and engineering |
| topic | Datenverarbeitung Informatik Mathematik Computer science Mathematics Numerical analysis Data processing Numerische Mathematik (DE-588)4042805-9 gnd |
| topic_facet | Datenverarbeitung Informatik Mathematik Computer science Mathematics Numerical analysis Data processing Numerische Mathematik |
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