File:Kleene fixpoint.pdf
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Summary[edit]
| Description |
English: Computation of the least fixpoint of f(x) = 110x2+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 |
|---|
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
|
| C source for arrow coordinates |
|---|
#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;
}
|
Licensing[edit]
I, the copyright holder of this work, hereby publish it under the following license:
This file is licensed under the Creative Commons Attribution-Share Alike 4.0 International license.
- You are free:
- to share – to copy, distribute and transmit the work
- to remix – to adapt the work
- Under the following conditions:
- attribution – You must give appropriate credit, provide a link to the license, and indicate if changes were made. You may do so in any reasonable manner, but not in any way that suggests the licensor endorses you or your use.
- share alike – If you remix, transform, or build upon the material, you must distribute your contributions under the same or compatible license as the original.
File history
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| Date/Time | Thumbnail | Dimensions | User | Comment | |
|---|---|---|---|---|---|
| current | 17:42, 17 November 2020 |  | 1,379 × 1,264 (10 KB) | Jochen Burghardt (talk | contribs) | Uploaded own work with UploadWizard |
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