Lagrange/Hermite Interpolation

Write-up coming soon.

The full interpolations are the polynomials fitting all five data points. The basis functions are the individual pieces, where each one is controlled by a single node contributes exactly one data value or derivative to the sum.

Full interpolation

Basis functions
\(k\) = 5
\(k\) = 1
\(k\) = 2

Derivatives
\(g_1\) = 2.00
\(g_2\) = -1.00
\(g_3\) = -3.00
\(g_4\) = 1.00
\(g_5\) = -3.00