Gram-Schmidt Orthogonal Functions

#1 Опубликовано: 22.06.2016 01:32:27

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Not as clean as Mathcad, but can be done terms by terms.
Smath 5346 does not recognise the dot product integration.
I might have missed some coding for solving algo style.

Jean

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#2 Опубликовано: 22.06.2016 12:27:04

Jean Giraud

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... read more in the attached Smath document. Work sheet renamed
for easier retrieval. Though Mathcad 8/11 is the champion for creating
orthogonal polynomials, Smath will do as well with a bit more sweat !
The summarised application is inductive of what it can do for you.
More can be done ... assume you have a noisy data set and the project
requires a trigonometric fit. It would be easy to fit a Fourier polynomial
sin/cos function cleaned of noise. This is not offered in the work sheet.

Maybe collabs will find a way to instruct Smath accept the "dot integrator",
something that wiil result "Mathcad style", usefull for next Smath release.

Jean

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#3 Опубликовано: 23.06.2016 01:24:27

CBG

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some automation .

Best regards
Carlos

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#4 Опубликовано: 23.06.2016 11:48:33

CBG

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A small improvement.

I correct , because the " dot " function does not work correctly

Best Regards

Carlos.

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#5 Опубликовано: 23.06.2016 14:04:40

Jean Giraud

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Thanks, Carlos: Your 2nd version is OK.
Still, can't export the reduced components in visible form.
Will work again tonight.

Cheers, Jean

#6 Опубликовано: 23.06.2016 21:43:56

Jean Giraud

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Carlos,

Thanks again for your contribution. This "Reconciliation" is made a bit more
function style. Very interesting that Smath can build "kernel algo" like
Mathcad 8/11 [discovered after years !]. The symbolic expansion is not
convenient at all. Maple is not good companion in there ...
... thus PART 2 in the attached.

Jean

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#7 Опубликовано: 23.06.2016 23:54:20

Jean Giraud

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... final reconciliation ...
ASSUME:
1. The 'o' "Kernel algo" can build from any vector functions f(x).
2. That naturally the roots exist and can be found.
3. Then the 15 decimals Lagrange is adequate for applications.

Project done, nothng to be envious of Mathcad, just different.

Successful collaboration

Jean

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#8 Опубликовано: 24.06.2016 13:24:32

CBG

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Jean,

A small simplification in the manual part.

Best regards.

Carlos.

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#9 Опубликовано: 24.06.2016 14:18:59

Jean Giraud

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Thanks, Carlos.

Jean

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