kvadratuurireeglid

Kvadratuurireeglid, also known as quadrature rules or numerical integration formulas, are methods used in numerical analysis to approximate the definite integral of a function. Instead of finding the exact antiderivative, which can be impossible or difficult for many functions, quadrature rules replace the integrand with a simpler function, such as a polynomial, that can be integrated easily. The integral of this approximating function then serves as an approximation to the original integral.

The general form of a quadrature rule involves a weighted sum of the function's values evaluated at specific points, called nodes. The formula can be expressed as the integral from a to b of f(x) dx approximately equals the sum from i=0 to n of w_i * f(x_i), where w_i are the weights and x_i are the nodes. The choice of nodes and weights determines the accuracy and properties of the quadrature rule.

Common types of quadrature rules include Newton-Cotes formulas, which use equally spaced nodes, and Gaussian quadrature, which selects optimal node locations and weights to achieve higher accuracy for a given number of function evaluations. The degree of accuracy of a quadrature rule indicates the degree of polynomial that the rule can integrate exactly. Kvadratuurireeglid are fundamental tools in various scientific and engineering disciplines where the evaluation of integrals is required.