Pivotelement

The pivot element ( pivot of French, Dreh-/Angelpunkt ') is the element of a set of numbers, which is selected as the first of an algorithm (eg, Gaussian elimination procedure, quicksort or the simplex method ) to perform certain calculations.

This matrix algorithms such as the Gaussian elimination method can work, it is often necessary that elements exist nonzero. Depending on the algorithm is then optionally did not look for a non-vanishing, but also on the ( absolute value ) the largest in the respective row or column. The thus your selection of the element is then called Pivoting. The row in which the pivot element is, it is called the pivot row, the column of the pivot element is called the pivot column.

When sorting by quicksort the pivot element identifies the element that is selected as the division limit. Quicksort sorted (recursively) all elements of "left" and "right" from the pivot element. Optimal is the median element, which generates two equal parts lists.