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Numerical methods using Matlab

Author: J E T Penny; G R Lindfield
Publisher: Upper Saddle River, NJ : Prentice Hall, ©2000.
Edition/Format:   Print book : English : 2nd edView all editions and formats
Summary:

Suitable for Modern Numerical Methods courses for third and fourth years of study. Skillfully balancing rigor with practicality, this text on using MATLAB software explores how this computing  Read more...

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Document Type: Book
All Authors / Contributors: J E T Penny; G R Lindfield
ISBN: 0130126411 9780130126412
OCLC Number: 41674282
Description: xiii, 482 pages : illustrations ; 24 cm
Contents: 1.1 Software package Matlab 2 --
1.2 Matlab on personal computers and workstations 3 --
1.3 Matrices and matrix operations in Matlab 3 --
1.4 Using the Matlab operator / for matrix division 5 --
1.5 Manipulating the elements of a matrix 5 --
1.6 Transposing matrices 7 --
1.7 Special matrices 8 --
1.8 Generating matrices with specified element values 9 --
1.9 Some special matrix operations 9 --
1.10 Element-by-element operations 10 --
1.11 Data structures in Matlab 11 --
1.12 Input and output in Matlab 16 --
1.13 Matlab graphics 18 --
1.14 Three-dimensional graphics 25 --
1.15 Scripting in Matlab 28 --
1.16 Functions in Matlab 33 --
1.17 User-defined functions in Matlab 35 --
1.18 Some pitfalls in Matlab 36 --
1.19 Speeding up calculations in Matlab 38 --
2 Linear Equations and Eigensystems --
2.2 Linear equation systems 46 --
2.3 Matlab operators / and / for solving Ax = b 52 --
2.4 Accuracy of solutions and ill-conditioning 56 --
2.5 Elementary row operations 59 --
2.6 Solution of Ax = b by Guassian elimination 60 --
2.7 LU decomposition 62 --
2.8 Cholesky decomposition 66 --
2.9 QR decomposition 69 --
2.10 Singular value decomposition 73 --
2.11 Pseudo-inverse 76 --
2.12 Over- and under-determined systems 81 --
2.13 Iterative methods 90 --
2.14 Sparse matrices 91 --
2.15 Eigenvalue problem 100 --
2.16 Iterative methods for solving the eigenvalue problem 105 --
2.17 Matlab function eig 110 --
3 Solution of Non-linear Equations --
3.2 Nature of solutions to non-linear equations 123 --
3.3 Bisection algorithm 124 --
3.4 Iterative or fixed point methods 125 --
3.5 Convergence of iterative methods 126 --
3.6 Ranges for convergence and chaotic behavior 128 --
3.7 Newton's method 130 --
3.8 Schroder's method 135 --
3.9 Numerical problems 137 --
3.10 Matlab function fzero and comparative studies 140 --
3.11 Methods for finding all the roots of a polynomial 141 --
3.12 Bairstow's method 142 --
3.13 Laguerre's method 146 --
3.14 Solving systems of non-linear equations 147 --
3.15 Broyden's method for solving non-linear equations 151 --
3.16 Comparing the Newton and Broyden methods 154 --
4 Differentiation and Integration --
4.2 Numerical differentiation 160 --
4.3 Numerical integration 164 --
4.4 Simpson's rule 165 --
4.5 Newton--Cotes formulae 169 --
4.6 Romberg integration 171 --
4.7 Gaussian integration 173 --
4.8 Infinite ranges of integration 176 --
4.9 Gauss--Chebyshev formulae 181 --
4.10 Filon's sine and cosine formulae 182 --
4.11 Problems in the evaluation of integrals 186 --
4.12 Test integrals 188 --
4.13 Repeated integrals 190 --
4.14 Simpson's rule for repeated integrals 191 --
4.15 Gaussian integration for repeated integrals 193 --
5 Solution of Differential Equations --
5.2 Euler's method 203 --
5.3 Problem of stability 205 --
5.4 Trapezoidal method 208 --
5.5 Runge--Kutta methods 211 --
5.6 Predictor--corrector methods 215 --
5.7 Hamming's method and the use of error estimates 218 --
5.8 Error propagation in differential equations 221 --
5.9 Stability of particular numerical methods 221 --
5.10 Systems of simultaneous differential equations 225 --
5.11 Lorenz equations 228 --
5.12 Predator--prey problem 231 --
5.13 Differential equations applied to neural nets 233 --
5.14 Higher-order differential equations 236 --
5.15 Stiff equations 237 --
5.16 Special techniques 241 --
5.17 Extrapolation techniques 244 --
6 Boundary Value Problems --
6.1 Classification of second-order partial differential equations 251 --
6.2 Shooting method 252 --
6.3 Finite difference method 255 --
6.4 Two-point boundary value problems 257 --
6.5 Parabolic partial differential equations 264 --
6.6 Hyperbolic partial differential equations 268 --
6.7 Elliptic partial differential9 equations 271 --
7 Fitting Functions to Data --
7.2 Interpolation using polynomials 282 --
7.3 Interpolation using splines 286 --
7.4 Fourier analysis of discrete data 290 --
7.5 Multiple regression: least squares criterion 304 --
7.6 Diagnostics for model improvement 308 --
7.7 Analysis of residuals 314 --
7.8 Polynomial regression 316 --
7.9 Fitting other functions using least squares 322 --
7.10 Transforming data 324 --
8 Optimization Methods --
8.2 Linear programming problems 338 --
8.3 Optimizing single-variable functions 345 --
8.4 Conjugate gradient method 349 --
8.5 Conjugate gradient method for solving linear equation systems 355 --
8.6 Genetic algorithms 358 --
8.7 Simulated annealing 371 --
9 Applications of the Symbolic Toolbox --
9.1 Introduction to the Symbolic Toolbox 380 --
9.2 Symbolic variables and expressions 380 --
9.3 Variable precision arithmetic in symbolic calculations 386 --
9.4 Series expansion and summation 387 --
9.5 Manipulation of symbolic matrices 391 --
9.6 Symbolic methods for the solution of equations 397 --
9.7 Symbolic differentiation 398 --
9.8 Symbolic partial differentiation 400 --
9.9 Symbolic integration 401 --
9.10 Symbolic solution of ordinary differential equations 404 --
9.11 Laplace transform 410 --
9.12 Z-transform 412 --
9.13 Fourier transform methods 414 --
9.14 Linking symbolic and numerical processes 417 --
Appendix 1 Matrix Algebra --
A1.2 Matrices and vectors 428 --
A1.3 Some special matrices 429 --
A1.4 Determinants 430 --
A1.5 Matrix operations 430 --
A1.6 Complex matrices 432 --
A1.7 Matrix properties 433 --
A1.8 Some matrix relationships 433 --
A1.9 Eigenvalues 434 --
A1.10 Definition of norms 434 --
A1.11 Reduced row echelon form 435 --
A1.12 Differentiating matrices 436 --
Appendix 2 Error Analysis --
A2.2 Errors in arithmetic operations 438 --
A2.3 Errors in the solution of linear equation systems 440 --
Appendix 3 Special Maple Functions --
A3.2 Dirac delta function 446 --
A3.3 Unit step function 447 --
A3.4 Signum function 448 --
A3.5 Euler's constant 448 --
Appendix 4 Matlab Functions 450.
Responsibility: John Penny, George Lindfield.

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