Gauss-Kronrod Algorithm

The Gauss-Kronrod algorithm is a method for accurately estimating the total of a function over an interval—think of summing up an area under a curve. It builds on Gaussian quadrature by adding extra points (called Kronrod points) to improve precision without significantly increasing computation. The algorithm uses these points and their weights to approximate the integral, then compares different estimates to gauge the error. If needed, it subdivides the interval to refine the result. This approach balances efficiency with accuracy, making it effective for complex numerical integration tasks.