Abstract
A possible improvement of the Faddeev-Kublanovskaja-Faddeeva lower bound for the least singular value ofR by using additional information aboutR is discussed. A fast algorithm is given for calculating such a bound using the diagonal elements and the elements of largest modulus in each row ofR.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
D. K. Faddeev, W. N. Kublanovskaja, W. N. Faddeeva,Solution of linear algebraic systems with rectangular matrices, Proc Steklov Inst Math 96 (1968).
P.-Å. Wedin,On pseudoinverses of perturbed matrices, Lund University, Department of Computer Sciences, May 1969.
Å. Björck,Solving linear least squares problems by Gram-Schmidt orthogonalization, BIT 7 (1967), 1–21.
J. H. Wilkinson,The algebraic eigenvalue problem, Clarendon Press, Oxford 1965.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Karasalo, I. A criterion for truncation of theQR-decomposition algorithm for the singular linear least squares problem. BIT 14, 156–166 (1974). https://doi.org/10.1007/BF01932945
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01932945