Procedure Minimize;
// using Ridder's method.
var i:integer;
fl,fh,fm,fnew,xl,xh,xm,xnew,xnauwk,s,sign:extended;
function f(x:extended):extended;
begin
result:=sqr(x); //change into your function
end;
begin
fh:=f(1);
fl:=f(-1);
if ((fl>0) and (fh<0)) or ((fl<0) and (fh>0)) then begin
xl:=-1;
xh:=1;
i:=0;
xnauwk:=1e-8; // needed accuracy
while (abs(xl-xh)>xnauwk) and (i<600) do begin
//max 600 interations
xm:=(xl+xh)/2; // new point
fm:=f(xm);
s:=sqrt(fm*fm-fl*fh);
if (fl-fh)<0 then sign:=-1 else sign:=1;
xnew:=xm+(xm-xl)*sign*fm/s;
fnew:=f(xnew);
if fnew*fm<=0 then begin // root between fm and fnew
xl:=xm;
fl:=fm;
xh:=xnew;
fh:=fnew;
end else if fl*fnew<=0 then begin
xh:=xnew;
fh:=fnew;
end else if fh*fnew<=0 then begin
xl:=xnew;
fl:=fnew;
end else begin
writeln('Root not brackted, serious error');
// I use code to redirect standard output to a memo;
i:=600;end; // 600= maximum 3 of itterations
inc(i);
// writeln(fnew:8,' best result root
between ',fl:8,' and ',fh:8);
end;
// writeln('Root found in ',i,' iterations')
end
else
writeln('No root possible, serious error');
// I use code to redirect standard output to a memo;
end;
