<p> Tridiagonal System: [A, S] </p>

13b863de-b9a8-4d05-a19f-46022b425be0 4 6 5 decimal

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Matrix whose inverse will solve for the quadratic coeff's X A n X rows : i 13 n 1 - (* (range j 13 n 1 - (* (range M i j el 0 : for for i 1 n 1 - (range j 12 range k 13 range M 2 i * 1 - j + (3 i * 3 - k + (el X i 1 - j + el (k 1 -^: for for for i 2 n 1 - (range j 12 range k 12 range M 2 n 1 - (* i + 3 i * 8 - k + j 3 * + (el 1 - (j^- (2 X i el * (k 1 -^* : for for for M 13 el 1 : M 61 line :

X Y S n X rows : i 13 n 1 - (* (range M i el 0 : for i 1 n 1 - (range j 01 range M 2 i 1 + (* 2 - j + el Y i j + el : for for M 41 line :

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 :

Quadratic/Holistic adapted Mathcad 11 jmG: 2021-05-16

data 1012 -^0.0079 0.1 0.012 0.2 0.022 0.3 0.048 0.4 0.167 0.5 162 mat :

X data 1 col : Y data 2 col : 12 mat support data . 14 black plot : 21 mat

4 appVersion 0.98.6179.21440 ≡

A X A :

S X Y S :

x f x C 2 el C 3 el x * + (* C 1 el + x C 5 el C 6 el x * + (* C 4 el + x C 8 el C 9 el x * + (* C 7 el + x C 11 el C 12 el x * + (* C 10 el + x C 14 el C 15 el x * + (* C 13 el + 51 mat :

C A 1 -^S * :

A 1 -^S * sometimes needed ≡ 11 line

isolate C C eval :

X data 1 col : Y data 2 col : 12 mat x Csp X Y x cinterp : x Asp X Y x ainterp : 31 sys

Collect piecewise plot for solving ...

x f 1 el x f 2 el x f 3 el x f 4 el x f 5 el data 0.4584 0.5 1 2 mat 7 1 sys

x h 10 x ≤ (x 0.5 ≤ (& cases :

Scalar companion interpolator ω 0 : t Q n X rows : i 1 n 1 - (range t X i 1 + el ≤ (t X i el ≥ (& ω 0 : j 02 range ω ω C 3 i * 2 - j + el t j^* + : for 21 line out range if for t Q ω : 31 line : 21 line

x f 5 el 0.5 - 0 ≡ x 0.375 0.5 solve 0.4584

x Q x h * x Csp x h * 0 0.0079 . 14 black 0.1 0.012 . 14 black 0.2 0.022 . 14 black 0.3 0.048 . 14 black 0.4 0.167 . 14 black 0.5 1 . 14 black 6 5 mat 3 1 sys

PROJECT NOTE ... 1. In this plot at right, plot Asp(x) the Akima cubic specific to Smath. It is the sole known application. 2. Another method exist: Hermite Cubic Draftsman spline ... NOT offered.