Numerical Methods
Contents
Interpolation/Extrapolation 
Numerical Integration/Derivatives 
Polynomials, Function Evaluation, Chebyshev Approximation 
Optimization 
Root Finding; NonLinear Equations 
Sources Key 
Function Name  Description  Source(s) 
bcucof  construct 2D bicubic  recipes 
bcuint  bicubic interpolation  recipes 
hunt  search a table when calls are correlated  recipes 
locate  search an ordered table by bisection  recipes 
polcoe, polcof  polynomial coefficeints from table of values  recipes 
polin2  2D polynomial interpolation  recipes 
polint  polynomial interpolation  recipes 
ratint  rational function interpolation  recipes 
splie2  construct 2D spline  recipes 
splin2  2D spline interpolation  recipes 
spline  construct a cubic spline  recipes 
splint  cubic spline interpolation  recipes 
YInterp  Lagrangian interpolation  Turbo (p. 145) 
Numerical Integration / Derivatives
Function Name  Description  Source(s) 
gaucof  quadrature weights from orthogonal polynomials  recipes 
gauher  weights and abscissas for GaussHermite quadrature  recipes 
gaujac  weights and abscissas for GaussJacobi quadrature  recipes 
gaulag  weights and abscissas for GaussLaguerre quadrature  recipes 
gauleg  weights and abscissas for GaussLegendre quadrature  recipes 
Gauss Legendre Quadrature Lab Report  
midinf  integrate a function on a semiinifinite interval  recipes 
midpnt  extended midpoint rule  recipes 
midsql, midsqu  integrate a function with lower (midsql) or upper (midsqu) squareroot singularity  recipes 
orthog  construct nonclassical orthogonal polynomials  recipes 
qgaus  integrate a function by Gaussian quadratures  recipes 
qromb  integrate using Romberg adaptive method  recipes 
qromo  integrate using open Romberg adaptive method  recipes 
qsimp  integrate using Simpon's rule  recipes 
qtrap  integrate using trapezoidal rule  recipes 
quad3d  integrate a function over a 3D space  recipes 
Quadrature  Commerical Package from Engineering Objects International  
SimpsonArea  Turbo (p. 145146)  
trapzd  trapezoidal rule  recipes 
Polynomials, Functional Evaluation, Chebyshev Approximation
Function Name  Description  Source(s) 
chder  derivative of a function already Chebyshev fitted  recipes 
chebev  Chebyshev polynomial evaluation  recipes 
chebft  fit a Chebyshev polynomial to a function  recipes 
chebpc  polynomial coefficients from a Chebyshev fit  recipes 
chint  integrate a function already Chebyshev fitted  recipes 
ddpoly  evaluate a polynomial and its derivatives  recipes 
eulsum  sum a series by Eulervan Wijngaarden algorithm  recipes 
pcshft  polynomial coefficients of a shifted polynomials  recipes 
poldiv  divide one polynomial by another  recipes 
Numerical Methods in Pascal pages
http://wwwrab.larc.nasa.gov/nmp/nmpIndex.htm#LinearProgramming
http://wwwrab.larc.nasa.gov/nmp/nmpIndex.htm#Optimization
Function Name / Category  Description  Source(s) 
amebsa  simulated annealing in continuous spaces  recipes 
amoeba  minimize in Ndimensions by downhill simplex method  recipes 
anneal  traveling salesman problem by simulated annearling  recipes 
brent  find minimum of a function by Brent's method  recipes 
dbrent  find minimum of a function using derivative information  recipes 
dfpmin  minimize in Ndimensions by variable metric method  recipes 
frprmn  minimize in Ndimensions by conjugate gradient  recipes 
golden  find minimum of a function by golden section search  recipes 
linmin  minimum of a function along a ray in Ndimensions  recipes 
Minimization of a function of several variables  TPmath2(minfunc)  
mnbrak  bracket the minimum of a function  recipes 
Optimum  Min/max of function using Newton's method  Turbo (p. 144145) 
powell  minimize in Ndimensions by Powells' method  recipes 
Round Robin  Round Robin scheduling by Engineeing Objects International  
Simplex and Marquardt minimization methods  TPmath1(optim)  
Simplex procedure using LPoptimizer  Implementation in Borland Pascal 7.0 without Assembler and Borland Delphi
2 http://www.netcologne.de/~ncweidenma/readme.htm 

Simplex Program  www.geocities.com/SiliconValley/2926/tpsrc/simpas.txt  
simplx  linear programming maximization of a linear function  recipes 
Root Finding; NonLinear Equations
Function  Math Description  Source(s) 
laguer  find a root of a polynomial by Laguerre's method  recipes 
mnewt  Newton's method for systems of equations  recipes 
root  Using Newton's method  Turbo (p. 144) 
qroot  complex or double root of a polynomial  recipes 
rtbis  find root of a function by bisection  recipes 
rtflsp  find root of a function by falseposition  recipes 
rtnewt  find root of a function by NewtonRaphson  recipes 
rtsafe  find root of a function by NewtonRaphson and bisection  recipes 
rtsec  find root of a function by secant method  recipes 
scrsho  graph a function to search for roots  recipes 
zbrac  outward search for brackets on roots  recipes 
zbrak  inward search for brackets on roots  recipes 
zbrent  find root of a function by Brent's method  recipes 
zroots  roots of a polynomial by Laguerre's method with deflation  recipes 
Source  Description/Location 
recipes  Numerical Recipes Pascal shareware version ftp://garbo.uwasa.fi/pc/turbopas/nrpas13.zip 
TPmath1 TPmath2 
Jean DeBord's TPMath www.unilim.fr/pages_perso/jean.debord/tpmath/tpmath.htm 
Turbo  Turbo Algorithms (C, Pascal, Basic, Prolog) Keith Weiskamp, Namir Shamas, Ron Pronk John Wiley, 1989 
Other resources:
Numerical Methods in Pascal: Finite Elements
http://wwwrab.larc.nasa.gov/nmp/nmpIndex.htm#FiniteElements
Numerical Methods in Pascal: Science and EngineeringModules
http://wwwrab.larc.nasa.gov/nmp/nmpIndex.htm#BlindedByScience
Links Verified 5 Oct 2000
Updated 16 Feb 2003
since 1 Nov 1998