Метод Логранжа (логарифмирование)

unit Unit1;
 
interface
 
uses
Windows, Messages, SysUtils, Variants, Classes, Graphics, Controls, Forms,
Dialogs, TeEngine, Series, ExtCtrls, TeeProcs, Chart;
 
type
TForm1 = class(TForm)
    Chart1: TChart;
    Chart2: TChart;
    Chart3: TChart;
    Series3: TLineSeries;
    Series2: TLineSeries;
    Series1: TLineSeries;
 
procedure FormCreate(Sender: TObject);
private
{ Private declarations }
public
{ Public declarations }
end;
const
xmin=-10;
xmax=10;
n=9; //число узлов
 
var
Form1: TForm1;
h,x1,x2,x3: real;
x,y: array [1..11] of real;
d: array [0..100] of real;
 
implementation
 
{$R *.dfm}
 
function yf(x: real): real;
begin
yf:=(2*x*x+5*x+4);
end;
 
function lag(xl, yl: array of real; xn: real; n1: integer): real;
var
i,j: integer;
lx,lj,p: real;
begin
lx:=0;
for j:=1 to n1 do
begin
lj:=1;
for i:=1 to n1 do
begin
if i<>j then
begin
p:=(xn-xl[i])/(xl[j]-xl[i]);
lj:=lj*p;
end;
end;
lx:=lx+yl[j]*lj;
end;
Result:=lx;
end;
 
 
procedure TForm1.FormCreate(Sender: TObject);
var
i,j: integer;
yl: real;
 
begin
h:=(xmax-xmin)/n;
 
x3:=xmin;
while x3<=xmax do
begin
Series1.AddXY(x3,yf(x3));
x3:=x3+1;
end;
 
x2:=xmin;
for i:=1 to n+1 do
begin
x[i]:=x2;
y[i]:=yf(x[i]);
x2:=x2+h;
end;
 
x3:=xmin;
j:=1;
while x3<=xmax do
begin
for i:=1 to n+1 do
Series2.AddXY(x3,lag(x,y,x3,n));
 
d[j]:=abs(yf(x3)-lag(x,y,x3,n));
Series3.AddXY(x3,d[j]);
x3:=x3+0.1;
j:=j+1;
end;
end;
 
end.

x,y: array [1..11] of real;
d: array [0..100] of real;

function lag(xl, yl: array of real; xn: real; n1: integer): real;

for j:=1 to n1 do
begin
lj:=1;
for i:=1 to n1 do

var
  Form1: TForm1;
const
xmin=-10;
xmax=10;
n=9; //число узлов
type mas=array of real;
var
h,x1,x2,x3: real;
x,y,d: mas;
implementation
 
{$R *.dfm}
function yf(x: real): real;
begin
yf:=(2*x*x+5*x+4);
end;
 
function lag(xl, yl: mas; xn: real; n1: integer): real;
var
i,j: integer;
lx,lj,p: real;
begin
lx:=0;
for j:=0 to n1-1 do
begin
lj:=1;
for i:=0 to n1-1 do
begin
if i<>j then
begin
p:=(xn-xl[i])/(xl[j]-xl[i]);
lj:=lj*p;
end;
end;
lx:=lx+yl[j]*lj;
end;
Result:=lx;
end;
 
 
procedure TForm1.FormCreate(Sender: TObject);
var
i,j: integer;
yl: real;
begin
h:=(xmax-xmin)/n;
 
x3:=xmin;
while x3<=xmax do
begin
Series1.AddXY(x3,yf(x3));
x3:=x3+1;
end;
 
x2:=xmin;
setlength(x,n+1);
setlength(y,n+1);
for i:=0 to n do
begin
x[i]:=x2;
y[i]:=yf(x[i]);
x2:=x2+h;
end;
 
x3:=xmin;
j:=1;
while x3<=xmax do
begin
for i:=1 to n+1 do
Series2.AddXY(x3,lag(x,y,x3,n));
setlength(d,j);
d[j-1]:=abs(yf(x3)-lag(x,y,x3,n));
Series3.AddXY(x3,d[j-1]);
x3:=x3+0.1;
j:=j+1;
end;
end;