Summary
LetA be anm×n matrix with known singular value decomposition. The computation of the singular value decomposition of a matrixà is considered, whereà is obtained by appending a row or a column toA whenm≧n or by deleting a row or a column fromA whenm>n. An algorithm is also presented for solving the updated least squares problemà y−b≈, obtained from the least squares problemAx−b by appending an equation, deleting an equation, appending an unknown, or deleting an unknown.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Bunch, J.R., Nielsen, C.P., Sorensen, D.C.: Rank-one modification of the symmetric eigenproblem. Numer. Math.31, 31–48 (1978)
Businger, P.A.: Updating a singular value decomposition. Nordisk Tidskr. Informations behandling (BIT)10, 376–397 (1970)
Golub, G.H.: Some modified matrix eigenvalue problems. SIAM Rev.15, 318–334 (1973)
Jennings, L.S., Osborne, M.R.: A direct error analysis for least squares. Numer. Math.22, 325–332 (1974)
Lawson, C.L., Hanson, R.J.: Solving least squares problems. New Jersey: Prentice-Hall 1974
Osborne, M.R.: On the computation of stepwise regressions. Austral. Comput. J.8, 61–68 (1976)
Stewart, G.W.: Introduction to matrix computations. New York: Academic Press 1973
Thompson, R.C.: The behavior of eigenvalues and singular values under perturbations of restricted rank. Linear Algebra and Appl.13, 69–78 (1976)
Wilkinson, J.H.: The algebraic eigenvalue problem. Oxford: Clarendon Press 1965
Author information
Authors and Affiliations
Additional information
This research was supported by NSF grants MCS 75-06510 and MCS 76-03139
Rights and permissions
About this article
Cite this article
Bunch, J.R., Nielsen, C.P. Updating the singular value decomposition. Numer. Math. 31, 111–129 (1978). https://doi.org/10.1007/BF01397471
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01397471