# What's the difference between [quadrature] and [approximate-integration]?

The tag is described as "Quadrature refers to techniques in numerical integration, such as Riemann sum approximations, Simpson's rule and Gaussian quadrature." is described as "Use this tag for questions related to approximate integration, which constitutes a broad family of algorithms for calculating the numerical value of a definite integral."

Is there any difference between these two tags? If not, should they be made tag synonyms?

• I guess it's clear that quadrature schemes (which typically use linear combinations of function evaluations, i.e. weighted point values) are a subset of approximate integration schemes. I don't recall seeing a Question about an approximate integration scheme that was not a quadrature scheme, but I'll take a quick look. Dec 5 '21 at 1:58
• By the numbers there is not a lot of overlap in usage of the two tags: 130 for quadrature, 205 for approximate-integration, and 9 for using both tags. It seems to me that while Questions tagged quadrature are somewhat focused on basic schemes of numerical integration, the approximate-integration tag takes in problems about convergence of a sequence of integrals and some other aspects that are not just about the particular numerical schemes. Dec 5 '21 at 2:07
• In fact, the word "quadrature" by itself can also be used for evaluating an integral by non-numerical means. mathworld.wolfram.com/Quadrature.html Dec 5 '21 at 15:06
• @GEdgar Then is it useful to have a tag for such an imprecisely defined term? Dec 5 '21 at 17:39
• My impression is that "quadrature" usually refers to a numerical integration scheme that is based on some sort of (possibly piecewise) polynomial interpolation. With this interpretation, Monte Carlo and quasi-Monte Carlo methods are not quadrature methods. Dec 6 '21 at 19:27