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PASSIVE APPROXIMATION AND OPTIMIZATION USING B-SPLINES
Linnaeus Univ, Dept Phys & Elect Engn, S-35195 Vaxjo, Sweden..
Lund Univ, Dept Elect & Informat Technol, Box 118, S-22100 Lund, Sweden..
KTH, School of Electrical Engineering and Computer Science (EECS).
Stockholm Univ, Dept Math, S-10691 Stockholm, Sweden..
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2019 (English)In: SIAM Journal on Applied Mathematics, ISSN 0036-1399, E-ISSN 1095-712X, Vol. 79, no 1, p. 436-458Article in journal (Refereed) Published
Abstract [en]

A passive approximation problem is formulated where the target function an arbitrary complex-valued continuous function defined on an proximation domain consisting of a finite union of closed and bounded tervals on the real axis. The norm used is a weighted L-p-norm where 1 p <= infinity. The approximating functions are Herglotz functions nerated by a measure with Holder continuous density in an arbitrary ighborhood of the approximation domain. Hence, the imaginary and the al parts of the approximating functions are Holder continuous nctions given by the density of the measure and its Hilbert transform, spectively. In practice, it is useful to employ finite B-spline pansions to represent the generating measure. The corresponding proximation problem can then be posed as a finite-dimensional convex timization problem which is amenable for numerical solution. A nstructive proof is given here showing that the convex cone of proximating functions generated by finite uniform B-spline expansions fixed arbitrary order (linear, quadratic, cubic, etc.) is dense in e convex cone of Herglotz functions which are locally Holder ntinuous in a neighborhood of the approximation domain, as mentioned ove. As an illustration, typical physical application examples are cluded regarding the passive approximation and optimization of a near system having metamaterial characteristics, as well as passive alization of optimal absorption of a dielectric small sphere over a nite bandwidth.

Place, publisher, year, edition, pages
SIAM PUBLICATIONS , 2019. Vol. 79, no 1, p. 436-458
Keywords [en]
approximation, Herglotz functions, B-splines, passive systems, convex optimization, sum rules
National Category
Computer and Information Sciences
Identifiers
URN: urn:nbn:se:kth:diva-247577DOI: 10.1137/17M1161026ISI: 000460127100021Scopus ID: 2-s2.0-85063407473OAI: oai:DiVA.org:kth-247577DiVA, id: diva2:1298710
Note

QC 20190325

Available from: 2019-03-25 Created: 2019-03-25 Last updated: 2019-05-16Bibliographically approved

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