<p> data </p>

fced449d-5611-4c73-af64-e6a0832d329e 19 6 12 decimal

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

data 03 - 0.2 2.951056 - 0.4 2.589484 - 0.6 1.581057 - 0.8 0.05423 1 1.5 1.2 2.112192 1.4 2.110927 1.6 1.8785 1.8 1.607987 2 1.363636 2.2 1.15897 2.4 0.991538 2.6 0.855127 2.8 0.743554 3 0.651639 3.2 0.575282 3.4 0.511303 3.6 0.457245 3.8 0.411207 4 0.371707 212 mat :

X 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 2.2 2.4 2.6 2.8 3 3.2 3.4 3.6 3.8 4211 mat :

Y 3 - 2.951056 - 2.589484 - 1.581057 - 0.05423 1.5 2.112192 2.110927 1.8785 1.607987 1.363636 1.15897 0.991538 0.855127 0.743554 0.651639 0.575282 0.511303 0.457245 0.411207 0.371707 211 mat :

t 10 - 0.0 0.1 0.3 0.5 0.7 0.9 1.1 1.3 1.5 1.7 1.9 2.1 2.3 2.5 2.7 2.9 3.1 3.3 3.5 3.7 3.9 4.1 10241 mat :

data rows 21

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 :

The vector of the control points 't' must be in ascending order

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Lagrange piecewise Quadratic [order 2] k x B1 k 4 el x - (2^k 4 el k 2 el - (k 4 el k 3 el - (* / : k x B2 k 4 el k 1 el - (k 3 el x - (2^* - k 4 el k 3 el - (k 3 el k 2 el - (* k 3 el k 1 el - (* / : k x B3 k 4 el k 1 el - (k 2 el x - (2^* k 4 el k 2 el - (k 3 el k 2 el - (* k 2 el k 1 el - (* / : 31 sys

Lagrange Quadratic Generatrix k x b k 1 el x ≤ (x k 2 el ≤ (& k x B1 k x B2 + k x B3 + k 2 el x ≤ (x k 3 el ≤ (& k x B1 k x B2 + k 3 el x ≤ (x k 4 el ≤ (& k x B1 0 if if if 11 line :

x t 1 el t t rows el t 1 el 0.01 + (range :

Lagrange poly from Quad knots. n x Bp t n el t n 1 + el t n 2 + el t n 3 + el 41 mat x b :

1 x Bp 2 x Bp 3 x Bp 4 x Bp 5 x Bp 6 x Bp 6 1 sys

1 x Bp 2 x Bp 3 x Bp 4 x Bp 5 x Bp 6 x Bp 61 sys

Tridiag of QuadCoeff r 1 X rows range : ii r j r M ii j el j X ii el Bp : for for 31 line

s M 1 -^Y * : 3.03 - 2.9809 - 2.6766 - 1.6755 - 0.0813 1.6214 2.19 2.136 1.8813 1.604 1.3585 1.1543 0.9877 0.852 0.7411 0.6497 0.5737 0.5101 0.4562 0.4106 0.3696 211 mat

XY data . 10 black plot : 11 line

Scalar spline Lagrange x L s j el j x Bp * (j 1 s rows sum :

x 05 0.01 range :

Spline i 1 x rows range vy i el x i el L eval : for x vy augment 21 line :

Spline Spline :

XY Spline 2 1 sys

rescue integrator vx Spline 1 col : vy Spline 2 col : x f vx vy x ainterp : 31 line

x f x 04 int 1.708

x c 10 x ≤ (x 4 ≤ (& cases :

h 0.001 :

x f x L :

classical infinitesimal 1rst derivative x deriv 0.5 x h - f x f - x h - (x - / x f x h - f - x x h - (- / + (* :

less noisy ... 10 decimals x h D1 x 2 h * + f - 8 x h + f * + 8 x h - f * - x 2 h * - f + 12 h * / :

piecewise linear of quadratic segments

x h D1 x c * 1 1 sys