pivoting

1 Pivoting

Pivoting is a process performed on a matrix in order to improve numerical stability.

Partial pivoting of an $n\times n$ matrix is the sorting of the rows of the matrix so that row $i$ contains the maximum absolute column value for column $i$, among all rows $i,\mathrm{\dots },n$. That is, we begin by swapping row 1 with the row that has the largest absolute value for the first column, then swap row 2 with the row that has the largest magnitude for the second column (among rows 2 and below), and so on.

Complete pivoting is a reordering of both rows and columns, using the same method as above. It is usually not necessary to ensure numerical stability.

Pivoting can be represented as multiplication by permutation matrices.

Title	pivoting
Canonical name	Pivoting
Date of creation	2013-03-22 12:06:54
Last modified on	2013-03-22 12:06:54
Owner	akrowne (2)
Last modified by	akrowne (2)
Numerical id	8
Author	akrowne (2)
Entry type	Algorithm
Classification	msc 65F35
Classification	msc 65F30
Synonym	total pivoting
Synonym	complete pivoting
Synonym	partial pivoting