polynomialFit

Least-squares quartic c[1] + c[2]x + ... + c[5]x^4 through 10 points (x, y)

FastSmoothBuildings.Utilities.polynomialFit, function (source)

Purpose

Least-squares fit of a quartic c₁ + c₂ x + … + c₅ x⁴ through 10 points (x_k, y_k).

Equations

The normal equations A c = b, with A_ij = ∑_k x_k^i+j−2 and b_i = ∑_k y_k x_kⁱ⁻¹, solved by Gaussian elimination without pivoting (the normal matrix is symmetric positive definite when at least five of the x_k differ) and back substitution.

Use

Called on parameters: the windows fit the solar transmittance and the absorptance of each pane, given at the incidence angles 0, 10, …, 90 degrees, as quartics in the cosine of the angle, and evaluate them with polynomial.

Revisions

• October 2026: moved from trano's FastModel.Utilities.