Polynomial evaluation
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Introduction
It is often useful to evaluate a polynomial at a given point. The method shown below allows to calculate it by using only multiplication and addition, without any power.
Horner's method
Only 1-degree polynomial are evaluated, e.g. 3.x^2 + 2.x + 1, can be written, by means of an astute factorization, ((3.x +2).x + 1).
program PolyTest;
type
// coef's rank = it's degree
TDegres = 0..10;
TPolynome = record
Deg: TDegres;
Coefs: array[TDegres] of Double;
end;
function PolyEval(const aPoly: TPolynome; X: Double): Double;
var
i: TDegres;
begin
with aPoly do
begin
Result := 0;
for i := Deg downto Low(Coefs) do
Result := Result * X + Coefs[i];
end;
End;
(* Exemples *)
var
P: TPolynome;
begin
P.Deg := 2;
P.Coefs[2] := 3;
P.Coefs[1] := 2;
P.Coefs[0] := 1;
WriteLn('P(',7,') = ', PolyEval(7):10:2);
P.Deg := 0;
P.Coefs[2] := 0;
P.Coefs[1] := 0;
P.Coefs[0] := 1;
WriteLn('P(',7,') = ', PolyEval(7):10:2);
EndSee also
[https://en.wikipedia.org/wiki/Horner%27s_method| Horner's method (wiki)]
From the Free Pascal wiki, page "Polynomial evaluation", as it stood on 2020-02-23 after a change by Trev, out of the wiki's dump of 2024-05-26. Copyright stays with the author who wrote it, according to the old wiki's Licensing page. If you have concerns about this material, message the admin.