Fortran Program For Secant Method Numerical Analysis
This disk included with Numerical Analysis, Seventh Edition by Burden and Faires contains a C, FORTRAN. Maple, Mathematica. SECANT METHOD. This program uses the Secant Method to approximate a root of the equation f(x) = 0. The sample problem uses f(x) = cosx − x. INPUT: p0 = 1. The Secant Method. The secant method is an algorithm used to approximate the roots of a given function f.The method is based on approximating f using secant lines. The Algorithm. The secant method algorithm requires the selection of two initial approximations x 0 and x 1, which may or may not bracket the desired root, but which are chosen reasonably close to the exact root. The program uses the secant formula (aforementioned in the mathematical derivation) to calculate the root of the entered function. Here’s a sample output of the above MATLAB code for secant method: Secant Method Numerical Example: Lets perform a numerical analysis of the above program of secant method in MATLAB.
This page contains a list of sample Fortran computer programs associated with our textbook. In the following table, each line/entry contains the program name, the page number where it can be found in the textbook, and a brief description.| Chapter 1 | ||
| elimit.f | 15-16 | Example of a slowly converging sequence |
| sqrt2.f | 16-17 | Example of a rapidly converging sequence |
| nest.f | 20-21 | Nested multiplication |
| Chapter 2 | ||
| epsi.f | 54 | Approximate value of machine precision |
| depsi.f | 54 | Approximate value of double precision machine precision |
| ex2s22.f | 57-58 | Loss of significance |
| unstab1.f | 64-65 | Example of an unstable sequence |
| unstab2.f | 65-66 | Example of another unstable sequence |
| instab.f | 66 | Example of numerical instability |
| Chapter 3 | ||
| ex1s31.f | 76-78 | Bisection method: roots of exp(x) = sin(x) |
| ex1s32.f | 81-83 | Newton's method example |
| ex2s32.f | 86 | Simple Newton's method |
| ex3s32.f | 86-87 | Implicit function example |
| ex1s33.f | 95 | Secant method example |
| ex3s34.f | 103-104 | Contractive mapping example |
| ex3s35.f | 114 | Horner's method example |
| ex6s35.f | 114-115 | Newton's method on a given polynomial |
| ex7s35.f | 119-120 | Bairstow's method example |
| laguerre.f | 123-124 | Laguerre's method example |
| Chapter 4 | ||
| forsub.f | 150 | Forward substitution example |
| bacsub.f | 150 | Backward substitution example |
| pforsub.f | 151 | Forward substitution for a permuted system |
| pbacsub.f | 151 | Backward substitution for a permuted system |
| genlu.f | 154 | General LU-factorization example |
| doolt.f | 155 | Doolittle's-factorization example |
| cholsky.f | 157-158 | Cholesky-factorization example |
| bgauss.f | 167 | Basic Gaussian elimination |
| pbgauss.f | 169 | Basic Gaussian elimination with pivoting |
| gauss.f | 171-172 | Gaussian elimination with scaled row pivoting |
| paxeb.f | 174-175 | Solves Lz = Pb and then Ux = z |
| yaec.f | 175 | Solves UT z = c and then LTPy = z |
| tri.f | 180 | Tridiagonal system solver |
| ex1s45.f | 199-200 | Neumann series example |
| ex2s45.f | 201 | Gaussian elimination followed by iterative improvement |
| ex1s46.f | 208-209 | Example of Jacobi and Gauss-Seidel methods |
| ex2s46.f | 211 | Richardson method example (with scaling) |
| jacobi.f | 212-213 | Jacobi method example (with scaling) |
| ex3s46.f | 217 | Gauss-Seidel method (with scaling) |
| ex6s46.f | 228-229 | Chebyshev acceleration example |
| steepd.f | 234 | Steepest descent method example |
| cg.f | 238 | Conjugate gradient method |
| pcg.f | 243-244 | Jacobi preconditioned conjugate gradient method |
| Chapter 5 | ||
| ex1s51.f | 259 | Power method example |
| poweracc.f | 259-260 | Power method with Aitken acceleration |
| ex2s51.f | 261 | Inverse power method example |
| ipoweracc.f | 261 | Inverse power method with Aitken acceleration |
| ex1s52.f | 268 | Schur factorization example |
| qrshif.f | 276-277 | Modified Gram-Schmidt example |
| ex1s53.f | 282-284 | QR-factorization using Householder transformations |
| ex2s55.f | 302-303 | QR-factorization example |
| ex3s55.f | 304 | Shifted QR-factorization example |
| Chapter 6 | ||
| coef.f | 309-311 | Coefficients in the Newton form of a polynomial |
| fft.f | 455-456 | Fast Fourier transform example |
| adapta.f | 461-463 | Adaptive approximation example |
| Chapter 7 | ||
| ex1s71.f | 466-467 | Derivative approximations: forward difference formula |
| ex2s71.f | 469 | Derivative approximation: central difference |
| ex5s71.f | 473 | Derivative approximation: Richardson extrapolation |
| ex6s71.f | 476 | Richardson extrapolation |
| gauss5.f | 496 | Gaussian five-point quadrature example |
| romberg.f | 504 | Romberg extrapolation |
| adapt.f | 511 | Adaptive quadrature |
| Chapter 8 | ||
| taylor.f | 531-532 | Taylor-series method |
| rk4.f | 542-543 | Runge-Kutta method |
| rkfelberg.f | Runge-Kutta-Fehlberg method | |
| taysys.f | 567-568 | Taylor series for systems |
| Chapter 9 | ||
| exs91.f | 618-619 | Boundary value problem (BVP): Explicit method example |
| exs92.f | 624-625 | BVP: Implicit method example |
| exs93.f | 632-633 | Finite difference method |
| ex3s96.f | 657 | BVP: Method of characteristics |
| mgrid1.f | 668-669 | Multigrid method example |
| exs98.f | 670 | Damping of errors |
| mgrid2.f | 674-675 | Multigrid method V-cycle |
The sample Fortran programs listed above can be found at the following anonymous ftp site:
Numerical Analysis Textbook Pdf
Numerical Analysis Problems And Solutions
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