archimedes.quadrature.golub_welsch_rule¶

archimedes.quadrature.golub_welsch_rule( measure: Measure, n: int, name: str | None = None, ) → QuadratureRule¶

Gauss quadrature rule for any Measure via its recurrence coefficients.

Unlike gauss_legendre() and friends, which use closed-form node/weight formulas (via scipy.special.roots_*) specific to their classical family, this works for any Measure subclass that implements recurrence_coeffs() – including, eventually, user-defined ones.

Parameters:

measure (Measure) – Measure to build the rule for.
n (int) – Number of quadrature nodes. Must be >= 1.
name (str, optional) – Name for the rule. Defaults to "golub_welsch_<MeasureClassName>".

Returns:

rule – Gauss quadrature rule with n nodes on measure.support, exact for polynomials up to degree 2n - 1.

Return type:

QuadratureRule

Raises:

ValueError – If n < 1.