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Passive Approximati...
Passive Approximation and Optimization Using B-Splines
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- Ivanenko, Yevhen (author)
- Linnaeus University,Linnéuniversitetet,Institutionen för fysik och elektroteknik (IFE),Linnaeus Univ, Dept Phys & Elect Engn, S-35195 Växjö, Sweden.
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- Gustafsson, Mats (author)
- Lund University,Lunds universitet,Teoretisk elektroteknik,Forskargrupper vid Lunds universitet,Electromagnetic Theory,Lund University Research Groups
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- Jonsson, B. Lars G. (author)
- KTH Royal Institute of Technology,KTH,Skolan för elektroteknik och datavetenskap (EECS),KTH Royal Instute of Technology, Sweden
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- Luger, Annemarie (author)
- Stockholm University,Stockholms universitet,Matematiska institutionen
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- Nilsson, Börje, 1949- (author)
- Linnaeus University,Linnéuniversitetet,Institutionen för matematik (MA),Linnaeus Univ, Dept Math, S-35195 Växjö, Sweden.
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- Nordebo, Sven, 1963- (author)
- Linnaeus University,Linnéuniversitetet,Institutionen för fysik och elektroteknik (IFE),Linnaeus Univ, Dept Phys & Elect Engn, S-35195 Växjö, Sweden.
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- Toft, Joachim, 1964- (author)
- Linnaeus University,Linnéuniversitetet,Institutionen för matematik (MA),Linnaeus Univ, Dept Math, S-35195 Växjö, Sweden.
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(creator_code:org_t)
- SIAM PUBLICATIONS, 2019
- 2019
- English.
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In: SIAM Journal on Applied Mathematics. - : SIAM PUBLICATIONS. - 0036-1399 .- 1095-712X. ; 79:1, s. 436-458
- Related links:
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http://dx.doi.org/10...
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https://urn.kb.se/re...
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https://doi.org/10.1...
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https://urn.kb.se/re...
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https://urn.kb.se/re...
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https://lup.lub.lu.s...
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Abstract
Subject headings
Close
- A passive approximation problem is formulated where the target function is an arbitrary complex-valued continuous function defined on an approximation domain consisting of a finite union of closed and bounded intervals on the real axis. The norm used is a weighted L-p-norm where 1 <= p <= infinity. The approximating functions are Herglotz functions generated by a measure with Holder continuous density in an arbitrary neighborhood of the approximation domain. Hence, the imaginary and the real parts of the approximating functions are Holder continuous functions given by the density of the measure and its Hilbert transform, respectively. In practice, it is useful to employ finite B-spline expansions to represent the generating measure. The corresponding approximation problem can then be posed as a finite-dimensional convex optimization problem which is amenable for numerical solution. A constructive proof is given here showing that the convex cone of approximating functions generated by finite uniform B-spline expansions of fixed arbitrary order (linear, quadratic, cubic, etc.) is dense in the convex cone of Herglotz functions which are locally Holder continuous in a neighborhood of the approximation domain, as mentioned above. As an illustration, typical physical application examples are included regarding the passive approximation and optimization of a linear system having metamaterial characteristics, as well as passive realization of optimal absorption of a dielectric small sphere over a finite bandwidth.
Subject headings
- NATURVETENSKAP -- Matematik (hsv//swe)
- NATURAL SCIENCES -- Mathematics (hsv//eng)
- NATURVETENSKAP -- Data- och informationsvetenskap (hsv//swe)
- NATURAL SCIENCES -- Computer and Information Sciences (hsv//eng)
- NATURVETENSKAP -- Matematik -- Matematisk analys (hsv//swe)
- NATURAL SCIENCES -- Mathematics -- Mathematical Analysis (hsv//eng)
- TEKNIK OCH TEKNOLOGIER -- Elektroteknik och elektronik (hsv//swe)
- ENGINEERING AND TECHNOLOGY -- Electrical Engineering, Electronic Engineering, Information Engineering (hsv//eng)
Keyword
- approximation
- Herglotz functions
- B-splines
- passive systems
- convex optimization
- sum rules
- Tillämpad matematik
- Applied Mathematics
- Approximation
- B-splines
- Convex optimization
- Herglotz functions
- Passive systems
- Sum rules
Publication and Content Type
- ref (subject category)
- art (subject category)
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To the university's database
- By the author/editor
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Ivanenko, Yevhen
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Gustafsson, Mats
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Jonsson, B. Lars ...
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Luger, Annemarie
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Nilsson, Börje, ...
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Nordebo, Sven, 1 ...
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show more...
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Toft, Joachim, 1 ...
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- About the subject
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- NATURAL SCIENCES
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NATURAL SCIENCES
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and Mathematics
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- NATURAL SCIENCES
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NATURAL SCIENCES
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and Computer and Inf ...
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- NATURAL SCIENCES
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NATURAL SCIENCES
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and Mathematics
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and Mathematical Ana ...
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- ENGINEERING AND TECHNOLOGY
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ENGINEERING AND ...
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and Electrical Engin ...
- Articles in the publication
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SIAM Journal on ...
- By the university
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Linnaeus University
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Royal Institute of Technology
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Stockholm University
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Lund University