GaussQuads

GaussQuads is a software library that provides routines for Gaussian quadrature, a class of numerical integration methods based on orthogonal polynomials. The core idea is to approximate an integral by a weighted sum of function values at specific nodes, chosen so the method is exact for polynomials up to a high degree. GaussQuads focuses on Gauss quadrature rules, especially Gauss-Legendre rules on the interval [-1,1], with facilities to transform these to arbitrary intervals [a,b].

The library generates quadrature nodes and weights for one-dimensional integration and can be extended to higher dimensions through tensor-product constructions or sparse-grid techniques. It typically includes support for different weight functions, such as those associated with Legendre, Jacobi, Laguerre, and Hermite polynomials, enabling a range of integration problems in physics and engineering.

GaussQuads emphasizes accuracy and efficiency, offering precomputed tables or fast algorithms to compute nodes and weights on demand, along with error estimation and adaptive refinement options in some implementations. It provides interfaces in multiple programming languages or exposes a clean API for integration into larger numerical workflows.

Applications of GaussQuads include numerical analysis, simulations in physics and engineering, and any context where precise evaluation of smooth integrands is required. The project is described as a practical, portable toolkit that can be integrated into scientific computing pipelines.