Re: Integration algorithm
Message #5 Posted by hugh on 3 July 2003, 2:20 p.m.,
in response to message #4 by Patrick
hi there,
recently ive been reviewing a bunch of quadrature algorithms. tooling up for version3 of my palm calculator. my search is along the lines of; what is the best numerical quadrature algorithm given a pocket device with a bit more poke than a normal calculator (poke=50-500Mhz).
candidates: simpsons rule, newton-cotes etc., romberg (open and closed), gauss and spectral techniques like clenshaw-curtis and other FFT accelerated forms.
BTW, does anyone have any code or doc for gauss-kronrod? i know what it is but i dont have enough details to write it (gauss-kronrod is adaptive gauss apparently now used by casio).
my test suite (so far)is: sqrt(x), cos(log(x)), exp(-x)/x, sqrt(fabs(x-1)), exp(-x*x), cos(1/x), sin
(x)/x.
the most promising so far is a modified romberg in the way suggested by kahan. i've come up with something that i think might well be very similar to the method used on the 15c. ok, you wont get the same answers, but algorithmically.
as a taunt i implemented it on the 9g, like this:
INPUT A,B,E
H=2;D=0;M=0;J=1;B=B-A
FOR (K=0;K<9;++K) {
L=D;F=H/2-1;C=0
FOR (I=0;I<J;++I) {
D=1-FF;X=((F+DF/2)*B+B)/2+A
GOSUB PROG 9;C=C+DY;F=F+H;}
F=4;D=M;M=(M+HC)/2
FOR (I=0;I<=K;++I) { C=N[I];N[I]=(F*M[I]-D)/(F-1);D=C;F=4F }
D=M[I]
IF (ABS(D-L) < 16E*ABS(D)) THEN { GOTO 1; }
J=2J;H=H/2 }
Lbl 1:
S=3DB/4;PRINT S
END
if you find this too worrying you can read it clearer here,
http://www.voidware.com/rombint.htm
| 
Go back to the main exhibit hall