Polynomials: Difference between revisions
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==Programming== | |||
[[Polynomial/Numerical Recipes]] - notes from Numerical Recipes on Polynomial and related classes | |||
==Fitting== | |||
To fit an Nth degree polynomial using N+1 points, can use linear algebra. | To fit an Nth degree polynomial using N+1 points, can use linear algebra. | ||
Revision as of 03:42, 8 April 2017
Programming
Polynomial/Numerical Recipes - notes from Numerical Recipes on Polynomial and related classes
Fitting
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.