00000cam a22000004i 4500 UP-1685594773861233394 Buklod 20070906150216.0 i|||||||||||||| | s| ||||||||||| 180130t20002000njua rb |||1 u|eng d 0130126411 (paper) (iLib)UPBAG-00000011622 BC-39919 Php3,870.00 DLC BAG rda eng QA 297 P45 2000 Penny, John (John E.T.) author. Numerical methods using MATLAB John Penny, George Lindfield. Second edition. Upper Saddle River, New Jersey Prentice Hall ©2000. xiii, 482 pages illustrations 24 cm Includes bibliographical references (pages 454-457) and index. 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. MATLAB. Numerical analysis Data processing. Lindfield, G. R. (George R.) author. FO UPBAG UPBAG-MAIN QA 297 P45 2000 Book