Numerical Methods for Bioinformatics
Part 1: Interpolation
Interpolation builds a function passing exactly through $(x_1,y_1),\ldots,(x_n,y_n)$. Different from curve fitting — no deviation allowed.
Weierstrass (1885): Any continuous function on [a,b] can be approximated to arbitrary precision by a polynomial. But which polynomial matters enormously.
Lagrange Interpolation
$$\pi_n(x) = \sum_i y_i \ell_i(x), \quad \ell_i(x) = \prod_{j \neq i} \frac{x - x_j}{x_i - x_j}$$
Error
[Description truncada. Veja o README completo no GitHub.]