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| Description
| - Pro mnohé účely koule nebo rotační elipsoid aproximují tvar Země poměrně dobře. Přesto však topografie Země způsobuje efekty, které stále stimulují značné vědecké úsilí. V protikladu ke konceptu tzv. parametru zmenšení v klasickém přístupu k těmto efektům, v tomto článku jsou využity postupné aproximace v rámci slabé formulace příslušných okrajových úloh. Vyšetřovány jsou funkcionálně analytické odhady pro objasnění konvergence iteračního procesu. Zejména je studována elipticita bilineární formy spojené s uvažovanou úlohou v oblasti řešení s elipsoidální hranicí. Aparát elipsoidálníh harmonických funkcí je podstatně využit k tomuto účelu. Odvozeny jsou kvantitativní odhady příslušných parametrů pro případ, že potenciál odpovídá modelu konečného stupně. (cs)
- For many purposes a sphere or an ellipsoid of revolution approximate the figure of the Earth fairly well. However, the Earth's topography causes effects that continuously stimulate a considerable research effort. In contrast to the concept of the so-called shrinking parameter in the classical treatment of the effect, successive approximations are applied within a weak formulation of the respective boundary-value problem in this paper. Functional-analytic estimates are investigated so as to clarify the convergence of the iteration process. In particular the ellipticity of a bilinear form associated with the problem under consideration is discussed for the solution domain of an ellipsoidal boundary. The apparatus of ellipsoidal harmonics is substantially used for this purpose. Quantitative estimates for the respective parameters were derived, when the potential is assumed to follow a finite degree model.
- For many purposes a sphere or an ellipsoid of revolution approximate the figure of the Earth fairly well. However, the Earth's topography causes effects that continuously stimulate a considerable research effort. In contrast to the concept of the so-called shrinking parameter in the classical treatment of the effect, successive approximations are applied within a weak formulation of the respective boundary-value problem in this paper. Functional-analytic estimates are investigated so as to clarify the convergence of the iteration process. In particular the ellipticity of a bilinear form associated with the problem under consideration is discussed for the solution domain of an ellipsoidal boundary. The apparatus of ellipsoidal harmonics is substantially used for this purpose. Quantitative estimates for the respective parameters were derived, when the potential is assumed to follow a finite degree model. (en)
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| Title
| - Successive approximations in the solution of weakly formulated geodetic boundary-value problem
- Postupné aproximace v řešení slabě formulované geodetické okrajové úlohy (cs)
- Successive approximations in the solution of weakly formulated geodetic boundary-value problem (en)
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| skos:prefLabel
| - Successive approximations in the solution of weakly formulated geodetic boundary-value problem
- Postupné aproximace v řešení slabě formulované geodetické okrajové úlohy (cs)
- Successive approximations in the solution of weakly formulated geodetic boundary-value problem (en)
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| skos:notation
| - RIV/00025615:_____/05:000012PH!RIV08-GA0-00025615
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| http://linked.open.../vavai/riv/strany
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| http://linked.open...avai/riv/aktivita
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| http://linked.open...avai/riv/aktivity
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| http://linked.open...vai/riv/dodaniDat
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| http://linked.open...aciTvurceVysledku
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| http://linked.open.../riv/druhVysledku
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| http://linked.open...iv/duvernostUdaju
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| http://linked.open...titaPredkladatele
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| http://linked.open...dnocenehoVysledku
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| http://linked.open...ai/riv/idVysledku
| - RIV/00025615:_____/05:000012PH
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| http://linked.open...riv/jazykVysledku
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| http://linked.open.../riv/klicovaSlova
| - Earth's gravity field, geodetic boundary-value problems, variational methods, functional-analytic estimates (en)
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| http://linked.open.../riv/klicoveSlovo
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| http://linked.open...ontrolniKodProRIV
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| http://linked.open...v/mistoKonaniAkce
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| http://linked.open...i/riv/mistoVydani
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| http://linked.open...i/riv/nazevZdroje
| - A Window on the Future of Geodesy, IAG Symposia, Vol. 128
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| http://linked.open...in/vavai/riv/obor
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| http://linked.open...ichTvurcuVysledku
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| http://linked.open...cetTvurcuVysledku
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| http://linked.open...vavai/riv/projekt
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| http://linked.open...UplatneniVysledku
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| http://linked.open...iv/tvurceVysledku
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| http://linked.open...vavai/riv/typAkce
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| http://linked.open.../riv/zahajeniAkce
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| number of pages
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| http://purl.org/ne...btex#hasPublisher
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| https://schema.org/isbn
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| is http://linked.open...avai/riv/vysledek
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