Riccati-like flows and matrix approximations

Uwe Helmke; Michael Prechtel; Mark A. Shayman

Kybernetika (1993)

  • Volume: 29, Issue: 6, page 563-582
  • ISSN: 0023-5954

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Helmke, Uwe, Prechtel, Michael, and Shayman, Mark A.. "Riccati-like flows and matrix approximations." Kybernetika 29.6 (1993): 563-582. <http://eudml.org/doc/28193>.

@article{Helmke1993,
author = {Helmke, Uwe, Prechtel, Michael, Shayman, Mark A.},
journal = {Kybernetika},
keywords = {best approximant; least squares problem; algebraic Riccati equation; symmetric matrices; gradient-like flows; dynamic Riccati equation; Riccati-like flows; phase portrait analysis; model reduction; linear control systems},
language = {eng},
number = {6},
pages = {563-582},
publisher = {Institute of Information Theory and Automation AS CR},
title = {Riccati-like flows and matrix approximations},
url = {http://eudml.org/doc/28193},
volume = {29},
year = {1993},
}

TY - JOUR
AU - Helmke, Uwe
AU - Prechtel, Michael
AU - Shayman, Mark A.
TI - Riccati-like flows and matrix approximations
JO - Kybernetika
PY - 1993
PB - Institute of Information Theory and Automation AS CR
VL - 29
IS - 6
SP - 563
EP - 582
LA - eng
KW - best approximant; least squares problem; algebraic Riccati equation; symmetric matrices; gradient-like flows; dynamic Riccati equation; Riccati-like flows; phase portrait analysis; model reduction; linear control systems
UR - http://eudml.org/doc/28193
ER -

References

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  1. G. Eckart, G. Young, The approximation of one matrix by another of lower rank, Psychometrika / (1936), 211-218. (1936) 
  2. G. H. Golub, C. Van Loan, An analysis of the total least squares problem, SIAM J. Numer. Anal. 17 (1980), 883-843. (1980) Zbl0468.65011MR0595451
  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. (1987) MR0882452
  4. U. Helmke, J. B. Moore, Optimization and Dynamical Systems, Springer-Verlag, Berlin 1993. (1993) MR1299725
  5. U. Helmke, M. A. Shayman, Critical points of matrix least squares distance functions, Linear Algebra Appl., to appear. Zbl0816.15026MR1317470
  6. N. J. Higham, Computing a nearest symmetric positive semidefinite matrix, Linear Algebra Appl. 103 (1988), 103-118. (1988) Zbl0649.65026MR0943997
  7. B. De Moor, J. David, Total linear least squares and the algebraic Riccati equation, Systems Control Lett. 5 (1992), 329-337. (1992) Zbl0763.93085MR1180311
  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. MR1282700

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