Polynomials

To fit an Nth degree polynomial using N+1 points, can use linear algebra.

Here's how it works: an Nth degree polynomial has N+1 coefficients.

Rather than treating x as the unknown, treat a, b, c, d, etc. as the unknowns.

Evaluate the value of the polynomial at the known N+1 points, which gives you an LHS and an RHS - a linear equation. 85 = 2 a + 4 b + 8 c + d

Now do that with all N+1 points, and you get N+1 equations, for the N+1 unknowns. Solve that matrix equation to get the coefficients of your Nth degree polynomial.