TaylorError.html

> restart;
Digits := 6;
nicelog := z -> if z < 10.0^(-Digits) then -Digits else log[10](z) fi;

>    nTerms := 150;
Eerror := vector(nTerms):
Erelerr := vector(nTerms):
Lerror := vector(nTerms):
Lrelerr := vector(nTerms):
Serror := vector(nTerms):
Srelerr := vector(nTerms):
for x in [0.01,0.1,0.2,0.5,1.0,2.0,5.0,10.0,100.0]
do
   Es := 1:
   Eterm := 1:
   Ls := (x-1)/(x+1):
   Ltop := (x-1)/(x+1):
   Ss := x:
   Sterm := x:
   for k from 1 to nTerms do
     Eterm := x * Eterm / k:
     Es := Es + Eterm:
     Eerror[k] := abs(exp(x) - Es):
     Erelerr[k] := Eerror[k]/abs(exp(x)):
     Ltop := Ltop*((x-1)/(x+1))^2:
     Lterm := Ltop/(2*k+1):
     Ls := Ls + Lterm:
     Lerror[k] := abs(log(x) - 2*Ls):
     Lrelerr[k] := Lerror[k]/abs(log(x)):
     Sterm := Sterm*(-x^2)/(4*k^2+2*k):
     Ss := Ss + Sterm:
     Serror[k] := abs(sin(x) - Ss):
     Srelerr[k] := Serror[k]/abs(sin(x)):
   od:
   print("x" = x);
   Elog:=-log10(Erelerr[nTerms]):
   Slog:=-log10(Srelerr[nTerms]):
   Llog:=-log10(Lrelerr[nTerms]):

plot( [seq([j,nicelog(Erelerr[j])], j=1..nTerms)], axes=FRAME,
       labels = ["Order of Partial Sum", "Relative Error of Partial Sum"] );
plot( [seq([j,nicelog(Lrelerr[j])], j=1..nTerms)], axes=FRAME,
       labels = ["Order of Partial Sum", "Relative Error of Partial Sum"] );
plot( [seq([j,nicelog(Srelerr[j])], j=1..nTerms)], axes=FRAME,
       labels = ["Order of Partial Sum", "Relative Error of Partial Sum"] );

od;

Plotting error, empty plot

>