Gaussian Quadrature
Gaussian quadrature is a numerical integration technique used to approximate definite integrals by selecting optimal points (nodes) and weights. It is based on orthogonal polynomials, such as Legendre polynomials, to achieve high accuracy with fewer function evaluations compared to methods like the trapezoidal rule. This makes it efficient for integrating smooth functions over finite intervals, especially in scientific computing and engineering applications.
Developers should learn Gaussian quadrature when working on numerical analysis, physics simulations, or engineering problems that require precise integration of smooth functions, as it reduces computational cost and error. It is particularly useful in finite element methods, computational fluid dynamics, and quantum mechanics, where integrals of polynomial-like functions are common. Mastery of this technique enhances performance in high-accuracy numerical computations.