File:Kleene fixpoint.pdf
Summary
| Description |
English: Computation of the least fixpoint of f(x) = 1/10x2+atan(x)+1 using the Kleene fixed-point theorem. |
| Date | |
| Source | Own work |
| Author | Jochen Burghardt |
| Other versions | File:Kleene fixpoint.pdf * File:Kleene fixpoint svg.svg |
Gnuplot source code |
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set xrange [0:7]
set yrange [0:7]
set grid
set key top left
set arrow nohead lc 4 from 0.000 , 0.000 to 0.000 , 1.000
set arrow nohead lc 4 from 0.000 , 1.000 to 1.000 , 1.000
set arrow nohead lc 4 from 1.000 , 1.000 to 1.000 , 1.885
set arrow nohead lc 4 from 1.000 , 1.885 to 1.885 , 1.885
set arrow nohead lc 4 from 1.885 , 1.885 to 1.885 , 2.439
set arrow nohead lc 4 from 1.885 , 2.439 to 2.439 , 2.439
set arrow nohead lc 4 from 2.439 , 2.439 to 2.439 , 2.776
set arrow nohead lc 4 from 2.439 , 2.776 to 2.776 , 2.776
set arrow nohead lc 4 from 2.776 , 2.776 to 2.776 , 2.996
set arrow nohead lc 4 from 2.776 , 2.996 to 2.996 , 2.996
set arrow nohead lc 4 from 2.996 , 2.996 to 2.996 , 3.146
set arrow nohead lc 4 from 2.996 , 3.146 to 3.146 , 3.146
set arrow nohead lc 4 from 3.146 , 3.146 to 3.146 , 3.253
set arrow nohead lc 4 from 3.146 , 3.253 to 3.253 , 3.253
set arrow nohead lc 4 from 3.253 , 3.253 to 3.253 , 3.331
set arrow nohead lc 4 from 3.253 , 3.331 to 3.331 , 3.331
set arrow nohead lc 4 from 3.331 , 3.331 to 3.331 , 3.388
set arrow nohead lc 4 from 3.331 , 3.388 to 3.388 , 3.388
set arrow nohead lc 4 from 3.388 , 3.388 to 3.388 , 3.432
set arrow nohead lc 4 from 3.388 , 3.432 to 3.432 , 3.432
set arrow nohead lc 4 from 3.432 , 3.432 to 3.432 , 3.465
set arrow nohead lc 4 from 3.432 , 3.465 to 3.465 , 3.465
set arrow nohead lc 4 from 3.465 , 3.465 to 3.465 , 3.491
set arrow nohead lc 4 from 3.465 , 3.491 to 3.491 , 3.491
set arrow nohead lc 4 from 3.491 , 3.491 to 3.491 , 3.510
set arrow nohead lc 4 from 3.491 , 3.510 to 3.510 , 3.510
set arrow nohead lc 4 from 3.510 , 3.510 to 3.510 , 3.525
set arrow nohead lc 4 from 3.510 , 3.525 to 3.525 , 3.525
set arrow nohead lc 4 from 3.525 , 3.525 to 3.525 , 3.537
set arrow nohead lc 4 from 3.525 , 3.537 to 3.537 , 3.537
set arrow nohead lc 4 from 3.537 , 3.537 to 3.537 , 3.546
set arrow nohead lc 4 from 3.537 , 3.546 to 3.546 , 3.546
set arrow nohead lc 4 from 3.546 , 3.546 to 3.546 , 3.554
set arrow nohead lc 4 from 3.546 , 3.554 to 3.554 , 3.554
set arrow nohead lc 4 from 3.554 , 3.554 to 3.554 , 3.559
set arrow nohead lc 4 from 3.554 , 3.559 to 3.559 , 3.559
set arrow nohead lc 4 from 3.559 , 3.559 to 3.559 , 3.564
set arrow nohead lc 4 from 3.559 , 3.564 to 3.564 , 3.564
set arrow nohead lc 4 from 3.564 , 3.564 to 3.564 , 3.567
set arrow nohead lc 4 from 3.564 , 3.567 to 3.567 , 3.567
plot x*x/10+atan(x)+1 with lines lw 2 title "f(x)"
replot x with lines
pause -1
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C source for arrow coordinates |
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#include <math.h>
#include <stdio.h>
double f(double x) {
return x*x/10+atan(x)+1;
}
int main(void) {
int i;
double xCur;
double xOld;
xCur = 0;
for (i=0; i<20; ++i) {
xOld = xCur;
xCur = f(xOld);
printf("set arrow from %5.3f , %5.3f to %5.3f , %5.3f\n",
xOld,xOld,xOld,xCur);
printf("set arrow from %5.3f , %5.3f to %5.3f , %5.3f\n",
xOld,xCur,xCur,xCur);
}
return 0;
}
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Licensing
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