efg's Delphi Math Functions: Numerical Methods

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)

Function Name	Description	Source(s)
gaucof	quadrature weights from orthogonal polynomials	recipes
gauher	weights and abscissas for Gauss-Hermite quadrature	recipes
gaujac	weights and abscissas for Gauss-Jacobi quadrature	recipes
gaulag	weights and abscissas for Gauss-Laguerre quadrature	recipes
gauleg	weights and abscissas for Gauss-Legendre quadrature	recipes
Gauss Legendre Quadrature Lab Report
midinf	integrate a function on a semi-inifinite interval	recipes
midpnt	extended midpoint rule	recipes
midsql, midsqu	integrate a function with lower (midsql) or upper (midsqu) square-root 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 www.engineeringobjects.com/Quadrature.htm
SimpsonArea		Turbo (p. 145-146)
trapzd	trapezoidal rule	recipes

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 Euler-van Wijngaarden algorithm	recipes
pcshft	polynomial coefficients of a shifted polynomials	recipes
poldiv	divide one polynomial by another	recipes

Function Name / Category	Description	Source(s)
amebsa	simulated annealing in continuous spaces	recipes
amoeba	minimize in N-dimensions 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 N-dimensions by variable metric method	recipes
frprmn	minimize in N-dimensions by conjugate gradient	recipes
golden	find minimum of a function by golden section search	recipes
linmin	minimum of a function along a ray in N-dimensions	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. 144-145)
powell	minimize in N-dimensions by Powells' method	recipes
Round Robin	Round Robin scheduling by Engineeing Objects International www.engineeringobjects.com/RndRobin.htm
Simplex and Marquardt minimization methods		TPmath1(optim)
Simplex procedure using LP-optimizer	Implementation in Borland Pascal 7.0 without Assembler and Borland Delphi 2 http://www.netcologne.de/~nc-weidenma/readme.htm
Simplex Program	www.geocities.com/SiliconValley/2926/tpsrc/simpas.txt
simplx	linear programming maximization of a linear function	recipes

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 false-position	recipes
rtnewt	find root of a function by Newton-Raphson	recipes
rtsafe	find root of a function by Newton-Raphson 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