Click here to see the number of accesses to this library.

file chap2.f for Chapter 2. The Solution of Nonlinear Equations f(x) = 0 , 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 file chap3.f for Chapter 3. The Solution of Linear Systems AX = B , 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 file chap4.f for Chapter 4. Interpolation and Polynomial Approximation , 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 file chap5.f for Chapter 5. Curve Fitting , 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 file chap6.f for Chapter 6. Numerical Differentiation , Algorithm 6.1 Differentiation using limits , Algorithm 6.2 Differentiation using extrapolation , Algorithm 6.3 Differentiation based on N+1 nodes file chap7.f for Chapter 7. Numerical Integration , Algorithm 7.1 Composite trapezoidal rule , Algorithm 7.2 Composite Simpson's rule , Algorithm 7.3 Recursive trapezoidal rule , Algorithm 7.4 Romberg integration , Algorithm 7.5 Adaptule , Algorithm 7.6 Gauss-Legendre quadrature file chap8.f for Chapter 8. Numerical Optimization , 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 file chap9.f for Chapter 9. Solution of Differential Equations , Algorithm 9.1 Euler's method , Algorithm 9.2 Heun's method , Algorithm 9.3 Taylor's method of order four , Algorithm 9.4 Runge-Kutta method of order four , Algorithm 9.5 Runge-Kutta-Fehlberg method RKF45 , Algorithm 9.6 Adams-Bashforth-Moulton method , Algorithm 9.7 Milne-Simpson method , Algorithm 9.8 Hamming's method , Algorithm 9.9 Linear shooting method , Algorithm 9.10 Finite difference method file chap10.f for Chapter 10. Solution of Partial Differential Equations , 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 file chap11.f for Chapter 11. Eigenvalues and Eigenvectors , 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 file readme