Numerical Analysis:
Mathematics of Scientific Computing
Third Edition
David Kincaid & Ward Cheney
Sample Fortran Computer Programs

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:

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  Last updated: 5/7/2003