On Nov. 20, Ramond Toy wrote:
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>Oops. I've uploaded a new version that fixes this.
>
>Unfortunately, it still takes a very long time. My original test used
>the default parameters and it converged very quickly. With your new
>parameters, I gave up after a minute or so.
>
>But I think the problem is with the integrand, 1/(1+sqrt(x)). I'm
>guessing the infinite slope at 0 is going to give lots of trouble.
>bromberg(g, 1/2, 1) returns instantly. bromberg(g,1/100,1) takes a
>little bit longer.
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The new version of bromberg.lisp,
http://common-lisp.net/~rtoy/maxima/bromberg.lisp
no longer gives a lisp error (gcl), but is extremely
slow (I stopped the calculation after 13 min)
if I ask for 20 digit precision for the same
integrand over (1/2, 1) interval.
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(%i1) load("c:/work2/bromberg.lisp");
(%o1) "c:/work2/bromberg.lisp"
(%i2) [brombergtol,brombergabs,brombergit,brombergmin];
(%o2) [1.0E-4,0.0,11,0]
(%i3) (brombergtol:0.0b0,brombergit:100)$
(%i4) brombergabs:1.0b-10;
(%o4) 1.0b-10
(%i5) g(x):= 1/(1+sqrt(x))$
(%i6) bromberg(g,1/2,1);
(%o6) 2.6909206998617b-1
(%i7) time(%);
(%o7) [0.02]
(%i8) tval : bfloat(2 - log(4)),fpprec:50;
(%o8) 6.1370563888010938116553575708364686384899973127949b-1
(%i9) brombergabs:1.0b-20;
(%o9) 1.0b-20
(%i10) bval : bromberg(g,1/2,1);
Maxima encountered a Lisp error:
Console interrupt.
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I stopped the calculation after 13 min.
Ted