首先科普下Pivoting的含義

一般翻譯為“主元”,在對矩陣做某種算法時(shí),首先進(jìn)行的部分元素.在線性規(guī)劃的單純形法中常見.
wiki的解釋如下：
Pivot element
（the first element distinct from zero in a matrix in echelon form）
The
pivot or pivot element is the element of a matrix,which is selected
first by an algorithm (e.g.Gaussian elimination,Quicksort,Simplex
algorithm),to do certain calculations with the matrix.
The above
mentioned matrix algorithms require an entry distinct from zero in pivot
position to work properly or at all respectively.Depending on the
algorithm either one (random) element distinct from zero or the element
with the greatest absolute value in a row or column is chosen.This is
called pivotization.The row containing the pivot element is called pivot
row,the pivot element's column is called pivot column.
Pivot element
in Quicksort means the element that is selected as boundary for
partitioning.Quicksort sorts all elements „left“ and „right“ of the
pivot element recursively.

區(qū)別：

（1）

complete pivoting（即full pivoting），就是在矩陣分解或高斯消元的過程中，主元是在未進(jìn)行變換的所有行和列之間進(jìn)行選擇。也就是需要同時(shí)進(jìn)行行交換和列交換。
（2）

partial pivoting就是只在當(dāng)前進(jìn)行變換的列中選擇主元，只需要進(jìn)行行交換

一般full pivoting相比partial pivoting更加穩(wěn)定，但是更麻煩，速度會(huì)慢。
就是速度和精度之間的問題。

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