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

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 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 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