एप्लाइड और कम्प्यूटेशनल गणित जर्नल

A Fast Algorithm for Computing High-dimensional Gauss Quadrature Rules

Abstract

Rustam Grillo*

Gauss quadrature rules are essential for numerical integration, especially in high-dimensional spaces. Traditional methods for computing these rules become computationally expensive and inefficient as the dimensionality increases. This article presents a novel fast algorithm for computing high-dimensional Gauss quadrature rules, significantly reducing computational complexity and improving efficiency. The proposed method leverages sparse grids, tensor decompositions, and adaptive strategies to handle the curse of dimensionality effectively.