Two-step Gram-Schmidt downdating methods

Jesse L. Barlow; Alicja Smoktunowicz; Hasan Erbay

doi:10.1117/12.448659

20 November 2001 Two-step Gram-Schmidt downdating methods

Jesse L. Barlow, Alicja Smoktunowicz, Hasan Erbay

Proceedings Volume 4474, Advanced Signal Processing Algorithms, Architectures, and Implementations XI; (2001) https://doi.org/10.1117/12.448659
Event: International Symposium on Optical Science and Technology, 2001, San Diego, CA, United States

Abstract

The problem of deleting a row from the QR factorization X = UR by Gram-Schmidt techniques is intimately connected to solving the least squares problem (formula available in paper) by classical iterative methods. Past approaches to this problem have focused upon accurate computation of the residual (formula available in paper), thereby finding a vector (formula available in paper) that is orthogonal to U. This work shows that it is also important to accurately compute the vector f and that it must be used in the downdating process to maintain good backward error in the new factorization. New algorithms are proposed based upon this observation.

Citation Download Citation

Jesse L. Barlow, Alicja Smoktunowicz, and Hasan Erbay "Two-step Gram-Schmidt downdating methods", Proc. SPIE 4474, Advanced Signal Processing Algorithms, Architectures, and Implementations XI, (20 November 2001); https://doi.org/10.1117/12.448659

ACCESS THE FULL ARTICLE

INSTITUTIONAL
Select your institution to access the SPIE Digital Library.

SELECT YOUR INSTITUTION

PERSONAL
Sign in with your SPIE account to access your personal subscriptions or to use specific features such as save to my library, sign up for alerts, save searches, etc.

PERSONAL SIGN IN

No SPIE Account? Create one

PURCHASE THIS CONTENT

SUBSCRIBE TO DIGITAL LIBRARY

50 downloads per 1-year subscription

Members: $195

Non-members: $335 ADD TO CART

25 downloads per 1 - year subscription

Members: $145

Non-members: $250 ADD TO CART

PURCHASE SINGLE ARTICLE

Includes PDF, HTML & Video, when available