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:
“Resorts advertised for waitresses, specifying that they “must appear in short clothes or no engagement.” Below a Gospel Guide column headed, “Where our Local Divines Will Hang Out Tomorrow,” was an account of spirited gun play at the Bon Ton. In Jeff Winney’s California Concert Hall, patrons “bucked the tiger” under the watchful eye of Kitty Crawhurst, popular “lady” gambler.”
—Administration in the State of Colo, U.S. public relief program (1935-1943)