[Scilab-users] Floating-point relative accuracy – HELP
David Brant
brantosaurus at hotmail.com
Thu Dec 14 21:54:41 CET 2017
Hello
I'm not fully conversant with Matlab, but offered to help my daughter
with a tutorial in Scilab ... and then Matlab!
Basically Matlab gives the 'expected' tutorial answer (n=17), and scilab
does not! Hopefully this is down to my lack of expertise, but i would
very much like understand why.
Does the problem require the use of floating-point relative accuracy
feature (%eps)?
Any help would be very much appreciated.
*** scilab output
n k S dif
0. 1. 1. 1.718281828459045
1. 1. 2. 0.718281828459045
2. 2. 2.5 0.218281828459045
3. 6. 2.666666666666667 0.051615161792379
4. 24. 2.708333333333333 0.009948495125712
5. 120. 2.716666666666666 0.001615161792379
6. 720. 2.718055555555555 0.000226272903490
7. 5040. 2.718253968253968 0.000027860205077
8. 40320. 2.71827876984127 0.000003058617775
9. 362880. 2.718281525573192 0.000000302885853
10. 3628800. 2.718281801146385 0.000000027312661
11. 39916800. 2.718281826198493 0.000000002260552
12. 479001600. 2.718281828286169 0.000000000172876
13. 6227020800. 2.718281828446759 0.000000000012286
14. 87178291200. 2.71828182845823 0.000000000000815
15. 1307674368000. 2.718281828458995 0.000000000000050
16. 20922789888000. 2.718281828459043 0.000000000000002
17. 355687428096000. 2.718281828459046 4.44089209850D-16
18. 6402373705728000. 2.718281828459046 4.44089209850D-16
19. 1.21645100409D+17 2.718281828459046 4.44089209850D-16
20. 2.43290200818D+18 2.718281828459046 4.44089209850D-16
*** matlab output
n k S dif
0 1 1 1.7183
1 1 2 0.71828
2 2 2.5 0.21828
3 6 2.6667 0.051615
4 24 2.70833 0.0099485
5 120 2.716667 0.001615162
6 720 2.718056 0.0002262729
7 5040 2.718254 2.7860205e-05
8 40320 2.71827877 3.05861778e-06
9 362880 2.718281526 3.028858533e-07
10 3628800 2.7182818011 2.7312661022e-08
11 39916800 2.7182818262 2.26055263397e-09
12 479001600 2.718281828286 1.728768239673e-10
13 6227020800 2.7182818284468 1.2286172079712e-11
14 87178291200 2.71828182845823 8.15347789284715e-13
15 1307674368000 2.718281828458995 5.062616992290714e-14
16 20922789888000 2.718281828459043 2.664535259100376e-15
17 355687428096000 2.718281828459046 0
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