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%ALGOS
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% NUMERICAL METHODS: MATLAB Programs, (c) John H. Mathews 1995
% To accompany the text:
% NUMERICAL METHODS for Mathematics, Science and Engineering, 2nd Ed, 1992
% Prentice Hall, Englewood Cliffs, New Jersey, 07632, U.S.A.
% Prentice Hall, Inc.; USA, Canada, Mexico ISBN 0-13-624990-6
% Prentice Hall, International Editions: ISBN 0-13-625047-5
% This free software is compliments of the author.
% E-mail address: mathews@fullerton.edu
%
% This free software is complements of the author.
%
% These functions are User Contributed Routines which are being distributed by
% The MathWorks, upon request, on an "as is" basis. A User Contributed Routine
% is not a product of The MathWorks and The MathWorks assumes no responsibility
% for any errors that may exist in these routines.
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% CONTENTS
%
% Chapter 1. Preliminaries
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% Theorem 1.1 Limits and Continuous Functions
% Theorem 1.2 Intermediate Value Theorem
% Theorem 1.3 Extreme Value Theorem for a Continuous Function
% Theorem 1.4 Differentiable function implies continuous function
% Theorem 1.5 Rolle's Theorem
% Theorem 1.6 Mean Value Theorem
% Theorem 1.7 Extreme Value Theorem for a Differentiable Function
% Theorem 1.8 Generalized Rolle's Theorem
% Theorem 1.9 First Fundamental Theorem
% Theorem 1.10 Second Fundamental Theorem
% Theorem 1.11 Mean Value Theorem for Integrals
% Theorem 1.12 Weighted Integral Mean Value Theorem
% Theorem 1.13 Taylor's Theorem
% Theorem 1.14 Horner's Method for Polynomial Evaluation
% Theorem 1.15 Geometric Series
% Theorem 1.16 Big "O" remainders for Taylor's Theorem
% Theorem 1.17 Remainder term for Taylor's Theorem
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% Chapter 2. The Solution of Nonlinear Equations f(x) = 0
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% Algorithm 2.1 Fixed Point Iteration
% Algorithm 2.2 Bisection Method
% Algorithm 2.3 False position or Regula Falsi Method
% Algorithm 2.4 Approximate Location of Roots
% Algorithm 2.5 Newton-Raphson Iteration
% Algorithm 2.6 Secant Method
% Algorithm 2.7 Steffensen's Acceleration
% Algorithm 2.8 Muller's Method
% Algorithm 2.9 Nonlinear Seidel Iteration
% Algorithm 2.10 Newton-Raphson Method in 2-Dimensions
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% Chapter 3. The Solution of Linear Systems AX = B
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% Algorithm 3.1 Back Substitution
% Algorithm 3.2 Upper-Triangularization Followed by Back Substitution
% Algorithm 3.3 PA = LU Factorization with Pivoting
% Algorithm 3.4 Jacobi Iteration
% Algorithm 3.5 Gauss-Seidel Iteration
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% Chapter 4. Interpolation and Polynomial Approximation
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% Algorithm 4.1 Evaluation of a Taylor Series
% Algorithm 4.2 Polynomial Calculus
% Algorithm 4.3 Lagrange Approximation
% Algorithm 4.4 Nested Multiplication with Multiple Centers
% Algorithm 4.5 Newton Interpolation Polynomial
% Algorithm 4.6 Chebyshev Approximation
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% Chapter 5. Curve Fitting
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% Algorithm 5.1 Least Squares Line
% Algorithm 5.2 Least Squares Polynomial
% Algorithm 5.3 Non-linear Curve Fitting
% Algorithm 5.4 Cubic Splines
% Algorithm 5.5 Trigonometric Polynomials
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% Chapter 6. Numerical Differentiation
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% Algorithm 6.1 Differentiation Using Limits
% Algorithm 6.2 Differentiation Using Extrapolation
% Algorithm 6.3 Differentiation Based on N+1 Nodes
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% Chapter 7. Numerical Integration
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% Algorithm 7.1 Composite Trapezoidal Rule
% Algorithm 7.2 Composite Simpson Rule
% Algorithm 7.3 Recursive Trapezoidal Rule
% Algorithm 7.4 Romberg Integration
% Algorithm 7.5 Adaptive Quadrature Using Simpson's Rule
% Algorithm 7.6 Gauss-Legendre Quadrature
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% Chapter 8. Numerical Optimization
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% Algorithm 8.1 Golden Search for a Minimum
% Algorithm 8.2 Nelder-Mead's Minimization Method
% Algorithm 8.3 Local Minimum Search Using Quadratic Interpolation
% Algorithm 8.4 Steepest Descent or Gradient Method
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% Chapter 9. Solution of Differential Equations
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% Algorithm 9.1 Euler's Method
% Algorithm 9.2 Heun's Method
% Algorithm 9.3 Taylor's Method of Order 4
% Algorithm 9.4 Runge-Kutta Method of Order 4
% Algorithm 9.5 Runge-Kutta-Fehlberg Method RKF45
% Algorithm 9.6 Adams-Bashforth-Moulton Method
% Algorithm 9.7 Milne-Simpson Method
% Algorithm 9.8 The Hamming Method
% Algorithm 9.9 Linear Shooting Method
% Algorithm 9.10 Finite-Difference Method
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% Chapter 10. Solution of Partial Differential Equations
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% Algorithm 10.1 Finite-Difference Solution for the Wave Equation
% Algorithm 10.2 Forward-Difference Method for the Heat Equation
% Algorithm 10.3 Crank-Nicholson Method for the Heat Equation
% Algorithm 10.4 Dirichlet Method for Laplace's Equation
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% Chapter 11. Eigenvalues and Eigenvectors
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% Algorithm 11.1 Power Method
% Algorithm 11.2 Shifted Inverse Power Method
% Algorithm 11.3 Jacobi Iteration for Eigenvalues and Eigenvectors
% Algorithm 11.4 Reduction to Tridiagonal Form
% Algorithm 11.5 The QL Method with Shifts
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