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From <vachevil-ba...@yahoo.com>
Subject [Math 1.1-rc2] Neville and DividedDifference Interpolators... weird values????
Date Thu, 15 Dec 2005 10:49:02 GMT
```Hello,

This is my first post on this list, so forgive me if this is the wrong way.

We are using the interpolator algorithms in version 1.1-RC2 of Commons-math.

We have a question about the results of the DividedDifferenceInterpolator and NevilleInterpolator
as they seem to be very very out of line in comparison with the results of the SplineInterpolator.

May be the author or someone who knows those algorithms could explain the results...

To give you a set of examples based on some UK rates.

Here are the values given to the algorithms:
Vertex(X)  Value(Y)
2          4.6950
7          4.7550
14         4.7763
30         4.7938
60         7.4250
90         7.0688
120        4.6825
150        6.5438
180        4.6275
210        4.6050
240        4.5819
270        4.5575
310        4.5438
360        4.5313

We try to interpolate from point 2 -> 360 (ie 1Y)

Both Neville and DividedDifference gives us some NEGATIVE VALUES which we just do not understand
how it could find those....

They both start to go badly wrong after point 240/270.

NEVILLE:
Vertex	Value
2	4.695
3	4.709933422214146
4	4.7232924330368464
5	4.735235132991724
6	4.74581109668252
7	4.755
8	4.762743546359981
9	4.768971415776979
10	4.773621906789763
11	4.77665789031614
12	4.7780786463172645
13	4.7779281085922526
14	4.7763
15	4.7733402998177854
16	4.769247446698966
17	4.764270644690903
18	4.758706605927844
19	4.752895031833053
20	4.7472131048633244
21	4.742069234923521
22	4.7378962784870846
23	4.735144424101184
24	4.734273915255748
25	4.735747760478751
26	4.7400245609137234
27	4.747551567468935
28	4.758758062833027
29	4.774049148162626
30	4.7938
31	4.818350649910715
32	4.848001327382693
33	4.883008395640834
34	4.923580900149241
35	4.969877740641826
36	5.022005469489051
37	5.08001671202313
38	5.143909198057306
39	5.213625388199416
40	5.2890526736305184
41	5.370024123751931
42	5.456319752456385
43	5.547668270710316
44	5.643749290605887
45	5.744195944014942
46	5.848597877417263
47	5.9565045833471775
48	6.067429028172449
49	6.180851535556198
50	6.296223884924905
51	6.412973584545169
52	6.530508279370197
53	6.648220254627737
54	6.76549099715888
55	6.881695777757577
56	6.996208219180938
57	7.108404816078354
58	7.21766937480269
59	7.32339734289932
60	7.425
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211	4.7217379108778365
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310	4.5438
311	-4.631491472180087
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313	-26.55944347325334
314	-39.44434052230259
315	-53.69566824815879
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338	-800.8495703790544
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342	-961.9706119920046
343	-996.1886991573373
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351	-1052.3680845056932
352	-1014.6291236919515
353	-961.9554596235488
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355	-804.1288584566825
356	-694.7224800568884
357	-561.8523758784667
358	-402.9251214159594
359	-215.138585614294

Many thanks

Benoit

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