A constrained approximation problem arising in parameter identification
We pose and solve an extremal problem in the Hardy class H 2 of the disc, involving the best approximation of a function on a subarc of the circle by a H 2 function, subject to a constraint on its imaginary part on the complementary arc. A constructive algorithm is presented for the computation of s...
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| Vydané v: | Linear algebra and its applications Ročník 351; s. 487 - 500 |
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| Hlavní autori: | , , , |
| Médium: | Journal Article |
| Jazyk: | English |
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01.08.2002
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| ISSN: | 0024-3795, 1873-1856 |
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| Abstract | We pose and solve an extremal problem in the Hardy class
H
2 of the disc, involving the best approximation of a function on a subarc of the circle by a
H
2 function, subject to a constraint on its imaginary part on the complementary arc. A constructive algorithm is presented for the computation of such a best approximant, and the method is illustrated by a numerical example. The whole problem is motivated by boundary parameter identification problems arising in non-destructive control. |
|---|---|
| AbstractList | We pose and solve an extremal problem in the Hardy class H-2 of the disc, involving the best approximation of a function on a subarc of the circle by a H-2 function, subject to a constraint on its imaginary part on the complementary arc. A constructive algorithm is presented for the computation of such a best approximant, and the method is illustrated by a numerical example. The whole problem is motivated by boundary parameter identification problems arising in non-destructive control We pose and solve an extremal problem in the Hardy class H 2 of the disc, involving the best approximation of a function on a subarc of the circle by a H 2 function, subject to a constraint on its imaginary part on the complementary arc. A constructive algorithm is presented for the computation of such a best approximant, and the method is illustrated by a numerical example. The whole problem is motivated by boundary parameter identification problems arising in non-destructive control. |
| Author | Partington, Jonathan R. Jacob, Birgit Leblond, Juliette Marmorat, Jean-Paul |
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| Cites_doi | 10.1109/9.623101 10.1088/0266-5611/15/1/012 10.1007/978-3-0348-8362-7_6 10.1016/0005-1098(95)00106-3 10.1007/s003659900062 10.1006/jmaa.1999.6358 10.1137/0331065 |
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| Keywords | 30E10 35R30 46E20 Laplace's equation Constrained approximation Parameter identification Extremal problem 41A29 Inverse problem |
| Language | English |
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| References | Baratchart, Leblond, Mandréa, Saff (BIB4) 1999; 15 Leblond, Partington (BIB14) 1999; 234 Chen, Gu (BIB11) 2000 Duren (BIB12) 1970 Mäkilä, Partington, Gustafsson (BIB15) 1995; 31 Brézis (BIB8) 1983 Baratchart, Leblond, Partington (BIB5) 1996; 12 Partington (BIB16) 1997; 17 Alpay, Baratchart, Leblond (BIB1) 1993; vol. 185 Baratchart, Leblond, Partington, Torkhani (BIB6) 1997; 42 I. Chalendar, J. Leblond, J.R. Partington, Approximation problems in some holomorphic spaces, with applications, Proc. IWOTA-2000 (Bordeaux), Birkhäuser, Basel, 2001, to appear Helton, Merino (BIB13) 1993; 31 Baratchart, Leblond (BIB3) 1998; 14 S. Chaabane, M. Jaoua, J. Leblond, Parameter identification for Laplace equation and approximation in Hardy classes, 2001, in preparation. A short version appeared in: Proc. 39th Conf. on Decision and Control (CDC), IEEE, Sydney, 2000, pp. 2005–2010 Andersson (BIB2) 1997 Beauzamy (BIB7) 1985 Helton (10.1016/S0024-3795(01)00445-1_BIB13) 1993; 31 Brézis (10.1016/S0024-3795(01)00445-1_BIB8) 1983 Baratchart (10.1016/S0024-3795(01)00445-1_BIB5) 1996; 12 10.1016/S0024-3795(01)00445-1_BIB9 Partington (10.1016/S0024-3795(01)00445-1_BIB16) 1997; 17 Mäkilä (10.1016/S0024-3795(01)00445-1_BIB15) 1995; 31 Baratchart (10.1016/S0024-3795(01)00445-1_BIB4) 1999; 15 Beauzamy (10.1016/S0024-3795(01)00445-1_BIB7) 1985 Chen (10.1016/S0024-3795(01)00445-1_BIB11) 2000 Alpay (10.1016/S0024-3795(01)00445-1_BIB1) 1993; vol. 185 Andersson (10.1016/S0024-3795(01)00445-1_BIB2) 1997 10.1016/S0024-3795(01)00445-1_BIB10 Leblond (10.1016/S0024-3795(01)00445-1_BIB14) 1999; 234 Baratchart (10.1016/S0024-3795(01)00445-1_BIB6) 1997; 42 Duren (10.1016/S0024-3795(01)00445-1_BIB12) 1970 Baratchart (10.1016/S0024-3795(01)00445-1_BIB3) 1998; 14 |
| References_xml | – year: 1985 ident: BIB7 publication-title: Introduction to Banach Spaces and Their Geometry, Mathematics Studies – volume: 17 year: 1997 ident: BIB16 publication-title: Interpolation, Identification and Sampling – volume: 12 start-page: 423 year: 1996 end-page: 436 ident: BIB5 article-title: Hardy approximation to publication-title: Constr. Approx. – volume: 234 start-page: 500 year: 1999 end-page: 513 ident: BIB14 article-title: Constrained approximation and interpolation in Hilbert function spaces publication-title: J. Math. Anal. Appl. – volume: 15 start-page: 79 year: 1999 end-page: 90 ident: BIB4 article-title: How can meromorphic approximation help to solve some 2D inverse problems for the Laplacian? publication-title: Inverse Problems – year: 1983 ident: BIB8 publication-title: Analyse Fonctionnelle – year: 1970 ident: BIB12 publication-title: Theory of – reference: I. Chalendar, J. Leblond, J.R. Partington, Approximation problems in some holomorphic spaces, with applications, Proc. IWOTA-2000 (Bordeaux), Birkhäuser, Basel, 2001, to appear – year: 1997 ident: BIB2 publication-title: Topics in Complex Analysis – year: 2000 ident: BIB11 publication-title: Control-oriented System Identification: An – volume: vol. 185 start-page: 563 year: 1993 end-page: 573 ident: BIB1 article-title: Some extremal problems linked with identification from partial frequency data publication-title: 10th Conference on Analysis and Optimization of Systems, Sophia-Antipolis 1992 – volume: 42 start-page: 1318 year: 1997 end-page: 1325 ident: BIB6 article-title: Robust identification from band-limited data publication-title: IEEE Trans. Automat. Control – reference: S. Chaabane, M. Jaoua, J. Leblond, Parameter identification for Laplace equation and approximation in Hardy classes, 2001, in preparation. A short version appeared in: Proc. 39th Conf. on Decision and Control (CDC), IEEE, Sydney, 2000, pp. 2005–2010 – volume: 31 start-page: 1379 year: 1993 end-page: 1415 ident: BIB13 article-title: Conditions for optimality over publication-title: SIAM J. Control Optim. – volume: 14 start-page: 41 year: 1998 end-page: 56 ident: BIB3 article-title: Hardy approximation to publication-title: Constr. Approx. – volume: 31 start-page: 1799 year: 1995 end-page: 1819 ident: BIB15 article-title: Worst-case control-relevant identification publication-title: Automatica – year: 1983 ident: 10.1016/S0024-3795(01)00445-1_BIB8 – volume: 17 year: 1997 ident: 10.1016/S0024-3795(01)00445-1_BIB16 – volume: 42 start-page: 1318 year: 1997 ident: 10.1016/S0024-3795(01)00445-1_BIB6 article-title: Robust identification from band-limited data publication-title: IEEE Trans. Automat. Control doi: 10.1109/9.623101 – year: 1997 ident: 10.1016/S0024-3795(01)00445-1_BIB2 – volume: 15 start-page: 79 year: 1999 ident: 10.1016/S0024-3795(01)00445-1_BIB4 article-title: How can meromorphic approximation help to solve some 2D inverse problems for the Laplacian? publication-title: Inverse Problems doi: 10.1088/0266-5611/15/1/012 – ident: 10.1016/S0024-3795(01)00445-1_BIB10 doi: 10.1007/978-3-0348-8362-7_6 – year: 2000 ident: 10.1016/S0024-3795(01)00445-1_BIB11 – volume: vol. 185 start-page: 563 year: 1993 ident: 10.1016/S0024-3795(01)00445-1_BIB1 article-title: Some extremal problems linked with identification from partial frequency data – volume: 31 start-page: 1799 year: 1995 ident: 10.1016/S0024-3795(01)00445-1_BIB15 article-title: Worst-case control-relevant identification publication-title: Automatica doi: 10.1016/0005-1098(95)00106-3 – volume: 14 start-page: 41 year: 1998 ident: 10.1016/S0024-3795(01)00445-1_BIB3 article-title: Hardy approximation to Lp functions on subsets of the circle with 1⩽p<∞ publication-title: Constr. Approx. doi: 10.1007/s003659900062 – ident: 10.1016/S0024-3795(01)00445-1_BIB9 – volume: 12 start-page: 423 issue: 3 year: 1996 ident: 10.1016/S0024-3795(01)00445-1_BIB5 article-title: Hardy approximation to L∞ functions on subsets of the circle publication-title: Constr. Approx. – year: 1970 ident: 10.1016/S0024-3795(01)00445-1_BIB12 – year: 1985 ident: 10.1016/S0024-3795(01)00445-1_BIB7 – volume: 234 start-page: 500 year: 1999 ident: 10.1016/S0024-3795(01)00445-1_BIB14 article-title: Constrained approximation and interpolation in Hilbert function spaces publication-title: J. Math. Anal. Appl. doi: 10.1006/jmaa.1999.6358 – volume: 31 start-page: 1379 year: 1993 ident: 10.1016/S0024-3795(01)00445-1_BIB13 article-title: Conditions for optimality over H∞ publication-title: SIAM J. Control Optim. doi: 10.1137/0331065 |
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| Snippet | We pose and solve an extremal problem in the Hardy class
H
2 of the disc, involving the best approximation of a function on a subarc of the circle by a
H
2... We pose and solve an extremal problem in the Hardy class H-2 of the disc, involving the best approximation of a function on a subarc of the circle by a H-2... |
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| SubjectTerms | Constrained approximation domain_math.appl Extremal problem Inverse problem Laplace's equation Mathematics Parameter identification |
| Title | A constrained approximation problem arising in parameter identification |
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