The Lagrange error bound quantifies the accuracy of polynomial interpolation using Lagrange polynomials. It states that the absolute error between the interpolating polynomial and the true function is less than or equal to a constant times the maximum absolute value of the nth derivative of the function on the interpolation interval, where n is the degree of the polynomial. The Lagrange error bound is essential in understanding the accuracy and convergence properties of Lagrange interpolation and provides theoretical guarantees for its performance in approximating functions.
