********************************* README.DOC ********************************** "Numerical Analysis Algorithms in C", Version 4.2 ******************************************************************************* This collection of algorithms was written for the text "Numerical Analysis", third and fourth edition, by Burden and Faires. If you have not purchased this software, but would like to, write or call us at: CARE-FREE SOFTWARE C/O HAROLD A. TOOMEY 464 NORTH 750 EAST LINDON, UT 84042 1-801-785-0464 The table below lists the file names of all of the algorithms. Print it out and use it as a quick reference. For detailed information on using these programs, see your User's Manual or read the file "usersman.doc." An order form is also provided at the end of this document. The file "naautil.c" is the most important file of all since it is used by every algorithm. Read the first half of this file and change the option flags to suit your needs. ******************************************************************************* -------------------------------------------------------------------------- CHAPTER 1 Mathematical Preliminaries -------------------------------------------------------------------------- COMPLEX.C - "Numerical Recipes in C" Complex Number Routines. EQEVAL.C - Equation Evaluator Routines GAUSSJ.C - "Numerical Recipes in C" Gauss-Jordan Matrix Solver. NAAUTIL.C - "Numerical Analysis Algorithms in C" Utilities I. (standard) NAAUTIL2.C - "Numerical Analysis Algorithms in C" Utilities II. (extended) NAAUTIL3.C - "Numerical Analysis Algorithms in C" Utilities III. (complex) ROUND.C - Rounds a floating point value to SIG significant digits. TRUNC.C - Truncates a floating point value to SIG significant digits. 011B.C* - Taylor Polynomial Approximation Algorithm 1.1B -------------------------------------------------------------------------- CHAPTER 2 Solutions of Equations in One Variable -------------------------------------------------------------------------- 021.C* - Bisection (or Binary-Search) Algorithm 2.1 022.C* - Fixed-Point Algorithm 2.2 023.C - Newton-Raphson Algorithm 2.3 024.C* - Secant Algorithm 2.4 024B.C* - Method of False Position (or Regula Falsi) Algorithm 2.4B 024C.C - Modified Newton-Raphson Method Algorithm 2.4C 025.C* - Steffensen Algorithm 2.5 026.C* - Horner Algorithm 2.6 027.C* - Mller Algorithm 2.7 028A.C* + Complex Polynomial Solver (CPOLY) Algorithm 2.8A -------------------------------------------------------------------------- CHAPTER 3 Interpolation and Polynomial Approximation -------------------------------------------------------------------------- 031.C* - Neville's Iterated Interpolation Algorithm 3.1 031B.C* - Neville's Iterated Interpolation Algorithm 3.1B (with rounding) 031C.C* - Aitken's Iterated Interpolation Algorithm 3.1C 032.C* - Newton's Interpolatory Divided-Difference Algorithm 3.2 Formula 033.C* - Hermite Interpolation Algorithm 3.3 034.C* - Natural Cubic Spline Algorithm 3.4 035.C* - Clamped Cubic Spline Algorithm 3.5 -------------------------------------------------------------------------- CHAPTER 4 Numerical Differentiation and Integration -------------------------------------------------------------------------- 040B1.C - 1st Derivative Approximation (for functions) Algorithm 4.0B1 040B2.C*- 1st Derivative Approximation Algorithm 4.0B2 (for tabulated data) 040B3.C - 1st Derivative Approximation Algorithm 4.0B3 (for functions w/TOL) 040C1.C - 2nd Derivative Approximation (for functions) Algorithm 4.0C1 040C2.C*- 2nd Derivative Approximation Algorithm 4.0C2 (for tabulated data) 040D1.C*- Richardson's Extrapolation Algorithm 4.0D1 040D2.C*- Richardson's Extrapolation (with rounding) Algorithm 4.0D2 041.C* - Composite Simpson's Rule Algorithm 4.1 041B.C* - Composite Trapezoidal Rule Algorithm 4.1B 041C.C* - Composite Midpoint Rule Algorithm 4.1C 041D.C* - Newton-Cotes Formulas for Integrals (8 total) Algorithm 4.1D 042.C* - Adaptive Quadrature Algorithm 4.2 043.C* - Romberg Algorithm 4.3 043B.C* - Gaussian Quadrature Algorithm 4.3B 044.C - Composite Simpson's Rule for Double Integrals Algorithm 4.4 044B.C - Composite Trapezoid Rule for Double Integrals Algorithm 4.4B 044C.C - Gaussian Quadrature for Double Integrals Algorithm 4.4C 045.C - Composite Simpson's Rule for Triple Integrals Algorithm 4.5 045B.C - Composite Trapezoid Rule for Triple Integrals Algorithm 4.5B 045C.C - Gaussian Quadrature for Triple Integrals Algorithm 4.5C -------------------------------------------------------------------------- CHAPTER 5 Initial-Value Problems for Ordinary Differential Equations -------------------------------------------------------------------------- 051.C* - Euler Algorithm 5.1 051B.C* - Midpoint, Modified Euler, and Heun's Methods Algorithm 5.1B 052.C* - Runge-Kutta (Order Four) Algorithm 5.2 053.C - Runge-Kutta-Fehlberg Algorithm 5.3 054.C* - Adam's Fourth-Order Predictor-Corrector Algorithm 5.4 054B.C* - Adams-Bashforth (all four) and Milne's Methods Algorithm 5.4B 054C.C* - Milne-Simpson Predictor-Corrector Algorithm 5.4C 055.C* - Adam's Variable Step-Size Predictor-Corrector Algorithm 5.5 056.C* + Extrapolation Algorithm 5.6 057.C - Runge-Kutta for Systems of Differential Algorithm 5.7 Equations 057B.C - Euler's Variable Step-Size for Systems Algorithm 5.7B 058.C - Trapezoidal with Newton Iteration Algorithm 5.8 -------------------------------------------------------------------------- CHAPTER 6 Direct Methods for Solving Linear Systems -------------------------------------------------------------------------- 060B.C* - Matrix Inverter Algorithm 6.0B 060C.C* - Determinant of a Matrix Algorithm 6.0C 060D.C* - Matrix Multiplier Algorithm 6.0D 061.C* - Gaussian Elimination with Backward Algorithm 6.1 Substitution 061B.C* - Gaussian Elimination with Backward Algorithm 6.1B Substitution (with rounding) 061C1.C* - Gauss-Jordan Method Algorithm 6.1C1 061C2.C* - Gauss-Jordan Method (with rounding) Algorithm 6.1C2 061D1.C* - Gaussian-Elimination - Gauss-Jordan Hybrid Algorithm 6.1D1 Method 061D2.C* - Gaussian-Elimination - Gauss-Jordan Hybrid Algorithm 6.1D2 Method (with rounding) 062.C* - Gaussian Elimination with Maximal Column Algorithm 6.2 Pivoting 062B.C* - Gaussian Elimination with Maximal Column Algorithm 6.2B Pivoting (with rounding) 063.C* - Gaussian Elimination with Scaled Column Algorithm 6.3 Pivoting 063B.C* - Gaussian Elimination with Scaled Column Algorithm 6.3B Pivoting (with rounding) 064.C* - Direct Factorization Algorithm 6.4 064B.C* - Direct Factorization which solves AX=B Algorithm 6.4B 064C.C* - Direct Factorization with Maximal Column Algorithm 6.4C Pivoting (3rd edition) 065.C* - LDLt Factorization Algorithm 6.5 065B.C* - LDLt Factorization which solves AX=B Algorithm 6.5B 066.C* - Choleski Algorithm 6.6 066B.C* - Choleski which solves AX=B Algorithm 6.6B 067.C* - Crout Reduction for Tridiagonal Linear Systems Algorithm 6.7 -------------------------------------------------------------------------- CHAPTER 7 Iterative Techniques in Matrix Algebra -------------------------------------------------------------------------- 070B.C* - Vector and Matrix Norms Algorithm 7.0B 071.C* - Jacobi Iterative Algorithm 7.1 072.C* - Gauss-Seidel Iterative Algorithm 7.2 073.C* - Successive Over Relaxation (SOR) Algorithm 7.3 074.C* - Iterative Refinement (with rounding) Algorithm 7.4 074B.C* - Iterative Refinement (single-precision) Algorithm 7.4B -------------------------------------------------------------------------- CHAPTER 8 Approximation Theory -------------------------------------------------------------------------- 080B.C* - Least-Squares Polynomial Approximation Algorithm 8.0B 081.C* + Fast Fourier Transformation Algorithm 8.1 -------------------------------------------------------------------------- CHAPTER 9 Approximating Eigenvalues -------------------------------------------------------------------------- 091.C* - Power Method Algorithm 9.1 091B.C* - Power Method with Aitken's Delta^2 Method Algorithm 9.1B 092.C* - Symmetric Power Method Algorithm 9.2 093.C* - Inverse Power Method Algorithm 9.3 094.C* - Wielandt's Deflation Algorithm 9.4 094B.C* - Wielandt's Deflation using Power Method for Algorithm 9.4B lambda1 095.C* - Householder Method Algorithm 9.5 095B.C* - Householder Method (3rd edition) Algorithm 9.5B 095C.C* - Householder Method for Non-Symmetric Matrices Algorithm 9.5C (Upper Hessenberg) 095D.C* - Householder Method (with rounding) Algorithm 9.5D 096.C* - QR Algorithm Algorithm 9.6 096B.C* - QL Algorithm (3rd edition) Algorithm 9.6B -------------------------------------------------------------------------- CHAPTER 10 Numerical Solutions of Nonlinear Systems of Equations -------------------------------------------------------------------------- 101.C - Newton's Method for Systems Algorithm 10.1 101A.C - Steffensen's Method for Systems Algorithm 10.1A 102.C - Broyden's Method for Systems Algorithm 10.2 103.C - Steepest Descent Method (with F(x) and J(x)) Algorithm 10.3 103B.C - Steepest Descent Method (with G(x) and Algorithm 10.3B gradG(x)) -------------------------------------------------------------------------- CHAPTER 11 Boundary-Value Problems for Ordinary Differential Equations -------------------------------------------------------------------------- 111.C - Linear Shooting Algorithm 11.1 112.C - Nonlinear Shooting with Newton's Method Algorithm 11.2 112B.C - Nonlinear Shooting with Secant Method Algorithm 11.2B 113.C - Linear Finite Difference Algorithm 11.3 113B.C - Linear Finite Difference Algorithm 11.3B (Richardson's Extrapolation) 114.C - Nonlinear Finite Difference Algorithm 11.4 114B.C - Nonlinear Finite Difference Algorithm 11.4B (Richardson's Extrapolation) 115.C - Piecewise Linear Rayleigh-Ritz Algorithm 11.5 116.C - Cubic Spline Rayleigh-Ritz Algorithm 11.6 -------------------------------------------------------------------------- CHAPTER 12 Numerical Solutions to Partial-Differential Equations -------------------------------------------------------------------------- 121.C - Poisson Equation Finite-Difference (Elliptic) Algorithm 12.1 122.C* - Heat Equation Backward-Difference (Parabolic) Algorithm 12.2 122B.C* - Heat Equation Forward-Difference (Parabolic) Algorithm 12.2B 122C.C* - Heat Equation Richardson's Method (Parabolic) Algorithm 12.2C 123.C* - Crank-Nicolson (Parabolic) Algorithm 12.3 124.C - Wave Equation Finite-Difference (Hyperbolic) Algorithm 12.4 125.C - Finite-Element Algorithm 12.5 126A.C - Parabolic Equations With Newton Iteration Algorithm 12.6A in 1-D 127A.C - Parabolic Equations With Newton Iteration Algorithm 12.7A in 2-D 128A.C - Elliptic Equations With Newton Iteration Algorithm 12.8A in 2-D 129A.C - Biharmonic Equation Using Gauss-Jordan Method Algorithm 12.9A ****************************************************************************** * Written by: Harold A. Toomey, CARE-FREE SOFTWARE, 3Q 1991, v4.2 * * Copyright (C) 1988-1991, Harold A. Toomey, All Rights Reserved. * ****************************************************************************** ORDER FORM "NUMERICAL ANALYSIS ALGORITHMS IN C" A complete set of 116 stand-alone C programs have been written for the text "Numerical Analysis", Burden & Faires, 3rd and 4th edition. These programs include ALL of the algorithms as well as all modifications required for most of the homework exercises. The C source code is thoroughly commented and easily modified. The same source code runs on MS-DOS, UNIX, VMS, the Macintosh, and more! For a FREE demo disk call 1-801-785-0464. TO ORDER CALL OR MAIL THIS FORM TO: CARE-FREE SOFTWARE C/O HAROLD A. 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