1 Pivoting

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

Partial pivoting of an n×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,,n. That is, we begin by swapping row 1 with the row that has the largest absolute valueMathworldPlanetmathPlanetmathPlanetmath 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 matricesMathworldPlanetmath.


  • 1 G. H. Golub, C. F. Loan, Matrix Computations, 3rd edition, Johns Hopkins, 1996.
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 AlgorithmMathworldPlanetmath
Classification msc 65F35
Classification msc 65F30
Synonym total pivoting
Synonym complete pivoting
Synonym partial pivoting