Optimal approximation of linear operators: a singular value decomposition approach

H.B. Siahaan; S. Weiland; A.A. Stoorvogel

Optimal approximation of linear operators: a singular value decomposition approach

H.B. Siahaan, S. Weiland, A.A. Stoorvogel

Onderzoeksoutput: Hoofdstuk in Boek/Rapport/Congresprocedure › Conferentiebijdrage › Academic › peer review

Samenvatting

The purpose of this paper is to propose a definition of a set of singular values and a singular value decomposition associated with a linear operator defined on arbitrary normed linear spaces. This generalizes the usual notion of singular values and singular value decompositions to operators defined on spaces equipped with the p-norm, where p is arbitrary. Basic properties of these generalized singular values are derived and the problem of optimal rank approximation of linear operators is investigated in this context. We give sufficient conditions for the existence of optimal rank approximants in the p-induced norm and discuss an application of generalized singular values for the identification of dynamical systems from data.

Originele taal-2	Engels
Titel	Proceedings 15th International Symposium on Mathematical Theory of Networks and Systems (MNTS'02, Notre Dame IN, USA, August 12-16, 2002), Session FM3
Redacteuren	D.S. Gilliam, J. Rosenthal
Plaats van productie	Notre Dame IN, USA
Uitgeverij	Univ. Notre Dame
Pagina's	580-590
Status	Gepubliceerd - 2002

Citeer dit

Siahaan, H. B., Weiland, S., & Stoorvogel, A. A. (2002). Optimal approximation of linear operators: a singular value decomposition approach. In D. S. Gilliam, & J. Rosenthal (editors), Proceedings 15th International Symposium on Mathematical Theory of Networks and Systems (MNTS'02, Notre Dame IN, USA, August 12-16, 2002), Session FM3 (blz. 580-590). Univ. Notre Dame.

Siahaan, H.B. ; Weiland, S. ; Stoorvogel, A.A. / Optimal approximation of linear operators: a singular value decomposition approach. Proceedings 15th International Symposium on Mathematical Theory of Networks and Systems (MNTS'02, Notre Dame IN, USA, August 12-16, 2002), Session FM3. redacteur / D.S. Gilliam ; J. Rosenthal. Notre Dame IN, USA : Univ. Notre Dame, 2002. blz. 580-590

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title = "Optimal approximation of linear operators: a singular value decomposition approach",

abstract = "The purpose of this paper is to propose a definition of a set of singular values and a singular value decomposition associated with a linear operator defined on arbitrary normed linear spaces. This generalizes the usual notion of singular values and singular value decompositions to operators defined on spaces equipped with the p-norm, where p is arbitrary. Basic properties of these generalized singular values are derived and the problem of optimal rank approximation of linear operators is investigated in this context. We give sufficient conditions for the existence of optimal rank approximants in the p-induced norm and discuss an application of generalized singular values for the identification of dynamical systems from data.",

author = "H.B. Siahaan and S. Weiland and A.A. Stoorvogel",

year = "2002",

language = "English",

pages = "580--590",

editor = "D.S. Gilliam and J. Rosenthal",

booktitle = "Proceedings 15th International Symposium on Mathematical Theory of Networks and Systems (MNTS'02, Notre Dame IN, USA, August 12-16, 2002), Session FM3",

publisher = "Univ. Notre Dame",

}

Siahaan, HB, Weiland, S & Stoorvogel, AA 2002, Optimal approximation of linear operators: a singular value decomposition approach. in DS Gilliam & J Rosenthal (uitgave), Proceedings 15th International Symposium on Mathematical Theory of Networks and Systems (MNTS'02, Notre Dame IN, USA, August 12-16, 2002), Session FM3. Univ. Notre Dame, Notre Dame IN, USA, blz. 580-590.

Optimal approximation of linear operators: a singular value decomposition approach. / Siahaan, H.B.; Weiland, S.; Stoorvogel, A.A.
Proceedings 15th International Symposium on Mathematical Theory of Networks and Systems (MNTS'02, Notre Dame IN, USA, August 12-16, 2002), Session FM3. uitgave / D.S. Gilliam; J. Rosenthal. Notre Dame IN, USA: Univ. Notre Dame, 2002. blz. 580-590.

Onderzoeksoutput: Hoofdstuk in Boek/Rapport/Congresprocedure › Conferentiebijdrage › Academic › peer review

TY - GEN

T1 - Optimal approximation of linear operators: a singular value decomposition approach

AU - Siahaan, H.B.

AU - Weiland, S.

AU - Stoorvogel, A.A.

PY - 2002

Y1 - 2002

N2 - The purpose of this paper is to propose a definition of a set of singular values and a singular value decomposition associated with a linear operator defined on arbitrary normed linear spaces. This generalizes the usual notion of singular values and singular value decompositions to operators defined on spaces equipped with the p-norm, where p is arbitrary. Basic properties of these generalized singular values are derived and the problem of optimal rank approximation of linear operators is investigated in this context. We give sufficient conditions for the existence of optimal rank approximants in the p-induced norm and discuss an application of generalized singular values for the identification of dynamical systems from data.

AB - The purpose of this paper is to propose a definition of a set of singular values and a singular value decomposition associated with a linear operator defined on arbitrary normed linear spaces. This generalizes the usual notion of singular values and singular value decompositions to operators defined on spaces equipped with the p-norm, where p is arbitrary. Basic properties of these generalized singular values are derived and the problem of optimal rank approximation of linear operators is investigated in this context. We give sufficient conditions for the existence of optimal rank approximants in the p-induced norm and discuss an application of generalized singular values for the identification of dynamical systems from data.

M3 - Conference contribution

SP - 580

EP - 590

BT - Proceedings 15th International Symposium on Mathematical Theory of Networks and Systems (MNTS'02, Notre Dame IN, USA, August 12-16, 2002), Session FM3

A2 - Gilliam, D.S.

A2 - Rosenthal, J.

PB - Univ. Notre Dame

CY - Notre Dame IN, USA

ER -

Siahaan HB, Weiland S, Stoorvogel AA. Optimal approximation of linear operators: a singular value decomposition approach. In Gilliam DS, Rosenthal J, redacteurs, Proceedings 15th International Symposium on Mathematical Theory of Networks and Systems (MNTS'02, Notre Dame IN, USA, August 12-16, 2002), Session FM3. Notre Dame IN, USA: Univ. Notre Dame. 2002. blz. 580-590

Optimal approximation of linear operators: a singular value decomposition approach

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