<p> plotG, discrete poly </p>

81a7e49e-d39e-44d3-8a61-68144a851a48 13 6 12 decimal

&[DATE] &[TIME] - &[FILENAME]

data char size clr plot k 1 data rows range r3 k el char : r4 k el size : r5 k el clr : 13 mat for data r3 r4 r5 augment 21 line :

Low High step x fnct inc U Low High step range : i 1 U rows range f i el U i el fnct : for U f augment 31 line :

DATA order Poly X DATA 1 col : Y DATA 2 col : x φ n 0 order range F n 1 + el x n^: for F 21 line : j 1 x φ length range i 1 X length range M i j el X i el φ j el : for for Φ M transpose M * : d M transpose Y * : b Φ 1 -^eval d * : 41 line b x φ 21 mat 51 line :

ε 1015 -^:

Poly order explorer =======

DATA ε 2113.3 1 2111.7 2 2109.2 3 2105.2 4 2099.4 5 2092.1 6 2084.7 7 2078.6 8 2075.1 9 2073.9 10 2074.1 11 2074.4 12207413 2072.5 14 2070.1 15 2067.2 16 2064.4 17206218 2060.5 19 2059.6 202 mat :

order 5 :

b DATA order Poly 1 el : x φ DATA order Poly 2 el : 21 sys

1. just a demo to reveal infeasibility. 2. ε=0 "Uncertainty", i.e: matrix singular

<= recast the scalar fit x fit b x φ * :

x φ 1 x x 2^x 3^x 4^x 5^61 mat

b 2111.888723 5.439893 4.060737 - 0.56404 0.031055 - 0.000609 61 mat

pts DATA . 12 black plot :

x c 10 x ≤ (x 20 ≤ (& cases :

NOTE: polynomials fit of whatever order, fit only data that have same polynomial

format than the attempted fir order. This simple polyfit is based on monomials.

Instead of monomials, they can be Chebyshev of lot more fitting capabilities.

Rational fractions is generally very successful if passing the fit through support

points makes sense. On that, Smath can't be completely made MCD GenfitMatrix

which GenfitMatrix takes noisy data. The core algorithm of GenfitMatrix is the

numerical Genfit(, , ,) not yet attempted coded in Smath.

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XY=>raw data, XW=>smoothed data, Cfit=> meshed spline export

pts x fit x c * 2 1 sys

β 2113.3 7698867.75 - 2325181.6 309845.84 - 18772.336 461.17 - 3643.464 - 1098.816 146.84 - 8.933 0.22066 - 111 mat :

Padé rational fraction
..... NORMALIZED .....
Mathcad GenfitMatrix x β f β 1 el β 2 el x * + β 3 el x 2^* + β 4 el x 3^* + β 5 el x 4^* + β 6 el x 5^* + 1 β 7 el x * + β 8 el x 2^* + β 9 el x 3^* + β 10 el x 4^* + β 11 el x 5^* + / :

XY=>raw data, XW=>smoothed data, Cfit=> meshed spline export

pts x β f x c * 2 1 sys