Projection approximations to the matrix scattering operators and relative convergence phenomenon

Petrusenko, I.V.; Sirenko, Yu.K.

dc.contributor.author	Petrusenko, I.V.
dc.contributor.author	Sirenko, Yu.K.
dc.date.accessioned	2017-05-24T11:30:42Z
dc.date.available	2017-05-24T11:30:42Z
dc.date.issued	2017-05-23
dc.identifier.citation	Petrusenko, I.V., (2004), Analytic – numerical analysis of waveguide bends, Electromagnetics, 24:237-254. 2. Petrusenko, I.V., (2004), Matrix operator technique for analysis of wave transformers, Proc. 10th Int. Conf. on Mathematical Methods in Electromagnetic Theory (MMET’04), Dnipropetrovs’k, pp. 118-120. 3. Petrusenko, I.V. and Sirenko, Yu.K., (2011), Fresnel formulae for scattering operators, Telecommunications and Radio Engineering, 70(9):749-758. 4. Petrusenko, I.V. and Sirenko, Yu.K., (2009), Generalization of the power conservation law for scalar mode-diffraction problems, Telecommunications and Radio Engineering, 68(16):1399-1410. 5. Mittra, R. and Lee, S.W., (1971), Analytical techniques in the theory of guided waves, New York, The Macmillan Company, - 327 p. 6. Gohberg, I.C. and Fel’dman, I.A., (2006), Convolution equations and projection methods for their solution (Translations of mathematical monographs), Providence, American Mathematical Society, - 261 p. (Translated from Russian). 7. Trenogin, V.A., (2002), Functional analysis, Phizmathlit, Moscow: 488 p. (in Russian). 8. Weyl, H., (1997), The classical groups: Their invariants and representations, Chichester, Princeton University Press, - 316 p. 9. Richtmyer, R.D., (1978), Principles of advanced mathematical physics. Vol. 1, New York - Heidelberg - Berlin, Springer-Verlag, - 422 p. 10. Petrusenko, I.V. and Dmitryuk, S.G., (1986), The method of solution of the generalized waveguide bifurcation problem, Padiotekhnika i Elektronika, 31(7):1285-1293 (in Russian). 11. Gribanov, Yu.I., (1959), On the complete continuity of matrix operators in vector spaces, Doklady Akademii Nauk SSSR, 129(5):975-978 (in Russian)	uk_UA
dc.identifier.issn	0040-2508 Print,1943-6009 Online
dc.identifier.uri	http://hdl.handle.net/123456789/2402
dc.description	Petrusenko, I.V., and Yu.K. Sirenko, “Projection approximations to the matrix scattering operators and relative convergence phenomenon”, Telecommunications and Radio Engineering, 70 (10): 843-856, 2011. (USA)	uk_UA
dc.description.abstract	A matrix‐operator model of the mode‐matching technique is examined for a scalar problem of mode diffraction on abrupt discontinuity in the waveguide. The convergence of approximations,which are found via a truncation procedure, to the matrix operators of mode reflection and transmission is studied analytically. Various estimates for these projection approximations are obtained. On the basis of these results, the unconditional and relative convergence phenomenaare analyzed. The impact of the “Mittra rule” upon the rate of convergence is validatedanalytically. The uniform‐convergence condition for scattering operatorapproximations is stated. Properties of the condition number for the truncated matrix‐operator equation arediscussed. The results thus obtained may well be used to substantiatea highly practically class of mathematical models related to the mode‐matching technique	uk_UA
dc.language.iso	en	uk_UA
dc.publisher	Begell House	uk_UA
dc.relation.ispartofseries	Telecommunications and Radio Engineering Международный научный журнал по проблемам телекоммуникационной техники и электроники. Публикуется издательством Begell House;2011 / Volume 70, Number 10
dc.subject	mode‐matching technique	uk_UA
dc.subject	Cayley transform	uk_UA
dc.subject	truncation procedure	uk_UA
dc.title	Projection approximations to the matrix scattering operators and relative convergence phenomenon	uk_UA
dc.type	Article	uk_UA