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
Zadeh's Rule Zadeh's Rule In mathematical optimization, Zadeh's rule (also known as Least-entered rule) is an algorithmic refinement of the simplex method for linear optimization. The rule was proposed around 1980 by Lotfi A. Zadeh, and has entered the folklore of convex optimization since then. Zadeh offered a reward of $1,000 to anyone who can show that the rule admits polynomially many iterations or to prove that there is a family of linear programs on which the pivoting rule requires subexponentially many iterations to find the optimum. Zadeh's rule belongs to the family of history-based improvement rules which, during a run of