Delphi Math Functions

Numerical Methods


Contents

Interpolation/Extrapolation
Numerical Integration/Derivatives
Polynomials, Function Evaluation, Chebyshev Approximation
Optimization
Root Finding; Non-Linear Equations
Sources Key

Interpolation/Extrapolation

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 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

 


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

 


Optimization

Numerical Methods in Pascal pages
http://www-rab.larc.nasa.gov/nmp/nmpIndex.htm#LinearProgramming
 
http://www-rab.larc.nasa.gov/nmp/nmpIndex.htm#Optimization 

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

Root Finding; Non-Linear 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 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

 


Sources Key

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 TurboAlgorithms.JPG (6242 bytes)
Turbo Algorithms
(C, Pascal, Basic, Prolog)
Keith Weiskamp, Namir Shamas, Ron Pronk
John Wiley, 1989

Other resources:

Numerical Methods in Pascal:  Finite Elements
http://www-rab.larc.nasa.gov/nmp/nmpIndex.htm#FiniteElements 

Numerical Methods in Pascal:  Science and EngineeringModules
http://www-rab.larc.nasa.gov/nmp/nmpIndex.htm#BlindedByScience 


Links Verified 5 Oct 2000
Updated 16 Feb 2003


since 1 Nov 1998