An alternative algorithm for the refinement of ULV decompositions
Yükleniyor...
Tarih
2005
Yazarlar
Dergi Başlığı
Dergi ISSN
Cilt Başlığı
Yayıncı
Siam Publications
Erişim Hakkı
info:eu-repo/semantics/closedAccess
Özet
The ULV decomposition ( ULVD) is an important member of a class of rank-revealing two-sided orthogonal decompositions used to approximate the singular value decomposition ( SVD). It is useful in applications of the SVD such as principal components where we are interested in approximating a matrix by one of lower rank. It can be updated and downdated much more quickly than an SVD. In many instances, the ULVD must be refined to improve the approximation it gives for the important right singular subspaces or to improve the matrix approximation. Present algorithms to perform this refinement require O( mn) operations if the rank of the matrix is k, where k is very close to 0 or n, but these algorithms require O( mn(2)) operations otherwise. Presented here is an alternative refinement algorithm that requires O( mn) operations no matter what the rank is. Our tests show that this new refinement algorithm produces similar improvement in matrix approximation and in the subspaces. We also propose slight improvements on the error bounds on subspaces and singular values computed by the ULVD.
Açıklama
Slapnicar, Ivan/0000-0002-8741-3988; Erbay, Hasan/0000-0002-7555-541X
Anahtar Kelimeler
subspace approximation, orthogonal decompositions, refinement
Kaynak
Siam Journal On Matrix Analysis And Applications
WoS Q Değeri
Q1
Scopus Q Değeri
Q2
Cilt
27
Sayı
1
Künye
closedAccess
