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Title: Riccati-like flows and matrix approximations (English)
Author: Helmke, Uwe
Author: Prechtel, Michael
Author: Shayman, Mark A.
Language: English
Journal: Kybernetika
ISSN: 0023-5954
Volume: 29
Issue: 6
Year: 1993
Pages: 563-582
Category: math
MSC: 34A30
MSC: 65F30
MSC: 93B11
MSC: 93B25
MSC: 93B40
MSC: 93C15
idZBL: Zbl 0802.65058
idMR: MR1264887
Date available: 2009-09-24T18:43:50Z
Last updated: 2012-06-06
Stable URL:
Reference: [1] G. Eckart, G. Young: The approximation of one matrix by another of lower rank.Psychometrika / (1936), 211-218.
Reference: [2] G. H. Golub, C. Van Loan: An analysis of the total least squares problem.SIAM J. Numer. Anal. 17 (1980), 883-843. Zbl 0468.65011, MR 0595451
Reference: [3] G. H. Golub A. Hoffmann, G. W. Stewart: A generalization of the Eckart-Young-Mirsky matrix approximation theorem.Linear Algebra Appl. 88/89 (1987), 317-327. MR 0882452
Reference: [4] U. Helmke, J. B. Moore: Optimization and Dynamical Systems.Springer-Verlag, Berlin 1993. MR 1299725
Reference: [5] U. Helmke, M. A. Shayman: Critical points of matrix least squares distance functions.Linear Algebra Appl., to appear. Zbl 0816.15026, MR 1317470
Reference: [6] N. J. Higham: Computing a nearest symmetric positive semidefinite matrix.Linear Algebra Appl. 103 (1988), 103-118. Zbl 0649.65026, MR 0943997
Reference: [7] B. De Moor, J. David: Total linear least squares and the algebraic Riccati equation.Systems Control Lett. 5 (1992), 329-337. Zbl 0763.93085, MR 1180311
Reference: [8] J. B. Moore R. E. Mahony, U. Helmke: Recursive gradient algorithms for eigenvalue and singular value decomposition.SIAM J. Matrix Anal. Appl., to appear. MR 1282700


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