An Introduction to Numerical Methods in C++,9780198506935

An Introduction to Numerical Methods in C++

by
Edition: Revised
ISBN13: 9780198506935
ISBN10: 0198506937
Format: Paperback
Pub. Date: 2000-06-22
Publisher(s): Oxford University Press
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Summary

Designed for the many applied mathematicians and engineers who wish to explore computerized numerical methods, this text explores the power of C++ as a tool for work in numerical methods. This revision of the successful first edition includes for the first time information on programming in Windows-based environments. In addition it includes new topics and methods throughout the text that clarify and enhance the treatment of the subject.

Table of Contents

Preliminaries
1(20)
Elementary input and output
1(4)
Strings
1(2)
Numbers
3(1)
Standard error output
4(1)
Comments
5(1)
Basic data types
6(2)
Integer types
6(1)
Floating point types
7(1)
Void type
8(1)
Derived types
8(3)
Constants
9(1)
Enumerations
9(1)
Structures
10(1)
Pointers
11(5)
Pointer to void
13(1)
Constants and pointers
13(1)
Pointers to structures
14(1)
Arrays
14(2)
References
16(1)
Preprocessor directives
17(2)
Token replacement
17(1)
Conditional directives
18(1)
File inclusion
18(1)
Keywords and identifiers
19(1)
Expressions, statements and functions
20(35)
Expressions
21(4)
Arithmetic expressions
21(1)
Relational expressions
22(1)
Logical expressions
22(1)
Bitwise expressions
22(1)
Comma expressions
23(1)
Other expressions
23(1)
Operator precedence
23(2)
Statements
25(3)
Declaration and initialization
25(1)
Assignments
26(1)
Compound assignments
26(1)
Increments and decrements
26(2)
Compound statements
28(2)
Scope
29(1)
Lifetime
30(1)
Conditional statements
30(7)
if-else statements
30(3)
while statements
33(1)
do statements
34(1)
for statements
34(1)
break and continue statements
34(1)
goto statements
35(1)
switch statements
36(1)
Functions
37(9)
Inline functions
41(1)
Passing arguments to functions
42(1)
Functions returning void
42(1)
Reference arguments
43(1)
Pointer arguments
44(1)
Overloading function names
44(1)
Function templates
45(1)
Recursive functions
46(3)
Static local variables
49(1)
Pointers and functions
50(1)
Function types
51(1)
The function main
52(3)
Errors, theorems and speed
55(14)
Truncation
55(1)
Rounding errors
55(2)
Quadratic equations
57(1)
Floating point equality
58(1)
Conditioning and stability
59(1)
Local and global errors
60(1)
Basic theorems
60(2)
Rates of convergence
62(1)
Reciprocals without division
63(1)
Speed of computation
64(1)
Speed and recursion
65(3)
Mistakes
68(1)
Roots of non-linear equations
69(25)
Bisection method
69(5)
Simple recursive procedure
69(1)
Refined recursive procedure
70(3)
Non-recursive procedure
73(1)
Regula falsi method
74(2)
Secant method
76(1)
Convergence
77(2)
Fixed point method
79(2)
Choice of fixed point function
81(1)
Newton's method
82(1)
Multiple roots
83(1)
Aitken's extrapolation
84(1)
Roots of polynomials
85(3)
Horner's algorithm
86(1)
Stability
87(1)
Maxima and minima of functions
88(3)
Some standard things
91(3)
Classes
94(26)
Complex numbers
94(10)
Declaration
95(1)
Implementation
96(3)
Friend functions
99(1)
Operator functions
100(3)
Complex roots of quadratic equations
103(1)
Class string
104(9)
Declaration
104(1)
Implementation
105(2)
Assignment
107(1)
Indexing
108(2)
Concatenation
110(2)
Input and output
112(1)
Example
112(1)
Static members
113(2)
Class arrays
115(4)
Array of complex numbers
116(1)
Array of strings
117(1)
Array template
118(1)
Classes and header files
119(1)
Derived classes and streams
120(25)
The base class duple
120(5)
The derived class point
121(3)
The derived class complex
124(1)
Derivation and access
125(2)
Class string revisited
127(4)
Streams
131(8)
The stream buffer
131(1)
Output streams
132(1)
Input streams
133(1)
Formatted input and output
133(4)
Tabulation
137(2)
File input and output
139(6)
Text files
141(2)
Binary files
143(2)
Integer arithmetic
145(26)
Prime numbers
145(6)
A table of primes
146(2)
Prime factors
148(2)
The greatest common divisor
150(1)
Rational numbers
151(9)
The class rational
152(5)
The harmonic numbers
157(1)
Bernoulli's numbers
158(2)
Congruences and residues
160(2)
Fermat's theorem
161(1)
Periodic sequences
162(1)
Random numbers
162(9)
Linear congruence generators
163(1)
Choice of parameters
164(2)
Sequential potency
166(2)
Practical generators
168(1)
Shuffling
169(1)
Example---Monte Carlo integration
170(1)
Tests of randomness
171(17)
Even distribution test
173(3)
Serial correlation test
176(1)
The spectral test
177(11)
Minimization process
179(3)
The case k = 2
182(1)
The case k = 3
183(4)
Results
187(1)
Vectors and matrices
188(16)
The class vector
188(7)
The class matrix
195(5)
Operations of linear algebra
200(4)
Direct solution of linear equations
204(23)
Gaussian elimination
205(3)
Algorithms
205(2)
Speed of computation
207(1)
Refinement
208(5)
Pivoting
208(2)
The case of the vanishing determinant
210(1)
Minimizing the arithmetic
210(1)
Refined gauss
211(1)
Improved speed
212(1)
Scaling
212(1)
Matrix decomposition
213(2)
Crout algorithm
215(5)
Simple Crout
215(2)
Speed
217(1)
Crout with pivoting
218(2)
The inverse matrix
220(2)
Tridiagonal equations
222(3)
Modular programming
225(2)
Errors in matrix manipulation
227(9)
Norms
227(3)
Convergence
230(1)
Error estimation
231(3)
Random perturbations
233(1)
Iterative refinement
234(2)
Iterative solutions of systems of equations
236(14)
Gauss-Jacobi iteration
236(3)
Gauss-Seidel iteration
239(2)
Jacobi and Seidel compared
241(1)
Successive over-relaxation
242(1)
Speed of computation
243(3)
Roots of systems of non-linear equations
246(4)
Matrix eigenvalue problems
250(30)
General theory
251(4)
Locating eigenvalues
252(2)
Eigenvalue stability and errors of computation
254(1)
The power method
255(6)
Inverse power method
261(2)
Jacobi rotation method
263(5)
Householder's method
268(12)
Reduction to tridiagonal form
269(4)
Francis diagonalization
273(7)
Interpolation and data fitting
280(25)
Lagrangian interpolation
281(8)
Lagrangian algorithm
282(1)
Errors of interpolation
283(3)
Neville's algorithm
286(2)
Divided differences
288(1)
Inverse interpolation
289(1)
Cubic spline piecewise interpolation
289(4)
Cubic spline routine
290(2)
Lagrange polynomial and cubic spline compared
292(1)
Data fitting
293(4)
Least squares approximation
294(2)
Other approximations
296(1)
Sorting
297(8)
Quicksort
299(3)
Heapsort
302(3)
Graphics
305(29)
Text mode
305(5)
Graphics mode
310(11)
Classes point and pixel
311(3)
Block size
314(2)
Opening and closing graphics mode
316(1)
Presentation
316(2)
Drawing a function
318(2)
Scanning the screen
320(1)
The complex plane: quadratic Julia sets
321(4)
Dynamic use of colour: the Mandelbrot set
325(3)
Bezier curves
328(6)
Differentiation and integration
334(23)
Differentiation
334(4)
Richardson extrapolation
338(1)
Integration
339(4)
Composite formulae
343(3)
Asymptotic errors
346(1)
Adaptive integration
347(2)
Romberg integration
349(5)
Improper integrals
354(1)
Multiple integrals
355(2)
Orthogonal polynomials
357(26)
The Gram-Schmidt process
357(2)
Zeros of orthogonal polynomials
359(1)
Particular systems
360(4)
Legendre polynomials
360(2)
Chebyshev polynomials
362(1)
Laguerre polynomials
363(1)
Hermite polynomials
364(1)
Approximation of functions
364(5)
Taylor approximation
366(1)
Legendre approximation
366(2)
Chebyshev approximation
368(1)
Minimax approximation
369(3)
Gaussian quadrature
372(11)
Computation of nodes
374(1)
Computation of weights
375(1)
Nodes and weights combined
376(4)
An example
380(3)
Differential equations
383(30)
Existence and uniqueness
383(2)
Stability and conditioning
385(2)
Euler's method
387(4)
Higher order methods
391(1)
Runge-kutta methods
392(7)
Convergence
395(1)
Adaptation
396(3)
Multiple-step methods
399(10)
Two-step midpoint method
399(5)
Other two-step methods
404(5)
Predictor-corrector methods
409(2)
Domain of existence
411(2)
More about differential equations
413(25)
Systems of ordinary differential equations
413(5)
Runge-Kutta method
414(1)
Lotka-Volterra equations
415(3)
Second-order initial value problems
418(2)
Second-order boundary value problems
420(8)
The shooting method
420(3)
The linear finite difference method
423(3)
Extrapolated linear finite difference method
426(1)
The non-linear finite difference method
426(2)
Variational methods
428(3)
Eigenvalue problems
431(2)
Partial differential equations
433(5)
Recursive data types---lists
438(33)
The base class list
441(7)
List of class template
448(3)
The travelling salesman
451(10)
Multiple byte integers
461(10)
Elements of Fourier analysis
471(10)
Fourier series
471(2)
Periodic functions
473(2)
Discrete Fourier transforms
475(1)
Fast Fourier transforms
476(5)
Addendum Programming in Windows 481(52)
A1 The Window classes TApplication and TWindow
483(4)
A2 The class TWindow and the function Paint
487(4)
A3 Programming mouse buttons
491(1)
A4 An input dialogue box
492(2)
A5 A multiple document interface
494(7)
A6 The class Tscreen
501(10)
A7 Drawing a function
511(4)
A8 Mapping the screen
515(1)
A9 Ordinary differential equations
516(7)
A10 Two simultaneous differential equations
523(10)
Bibliography 533(2)
Appendix A standard.h 535(2)
Appendix B restring.h 537(1)
Appendix C rational.h 538(1)
Appendix D random.h 539(1)
Appendix E vecmat.h 540(2)
Appendix F stdgraph.h 542(2)
Appendix G list.h 544(2)
Appendix H screen.h 546(3)
Index 549

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