Trapezoidal rule that Monte-Carlo integration is most likely a better choice, but for 2 and 3 dimensions, equispaced sampling is efficient. This is exploited in computational solid state physics where equispaced sampling over primitive cells in the reciprocal lattice is known as "Monkhorst-Pack integration". For various classes of functions that are not twice-differentiable, the trapezoidal rule has sharper bounds than Simpson's rule. The trapezoidal rule is one of a family of formulas for numerical integration called Newton–Cotes formulas, of which the midpoint rule is similar to the trapezoid rule. Simpson's rule is another member of the same family, and in general has
Plain meaning rule Plain meaning rule The plain meaning rule, also known as the literal rule, is one of three rules of statutory construction traditionally applied by English courts. The other two are the "mischief rule" and the "golden rule". The plain meaning rule dictates that statutes are to be interpreted using the ordinary meaning of the language of the statute. In other words, a statute is to be read word for word and is to be interpreted according to the ordinary meaning of the language, unless a statute explicitly defines some of its terms otherwise or unless the result would be cruel