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
Mischief rule Mischief rule The mischief rule is one of three rules of statutory interpretation traditionally applied by English courts. The other two are the "plain meaning rule" (also known as the "literal rule") and the "golden rule". The main aim of the rule is to determine the "mischief and defect" that the statute in question has set out to remedy, and what ruling would effectively implement this remedy. In applying the mischief rule, the court is essentially asking what part of the law did the law not cover, but was meant to be rectified by Parliament in passing the bill. The