Column Pivoting
QR decomposition with column pivoting introduces a permutation matrix P:
Column pivoting is useful when A is (nearly) rank deficient, or is suspected of being so. It can also improve numerical accuracy. P is usually chosen so that the diagonal elements of R are non-increasing: . This can be used to find the (numerical) rank of A at lower computational cost than a singular value decomposition, forming the basis of so-called rank-revealing QR algorithms.
Read more about this topic: QR Decomposition
Famous quotes containing the word column:
“Averageness is a quality we must put up with. Men march toward civilization in column formation, and by the time the van has learned to admire the masters the rear is drawing reluctantly away from the totem pole.”
—Frank Moore Colby (1865–1925)