| Attributes | Values |
|---|
| rdf:type
| |
| Description
| - The discussion starts with a general review of iteration concepts as applied for solving BVPs in gravity field studies. The subsequent explanations rest on the weak formulation of the problems. This enables a natural transition to an interpretation of the solution in terms of function bases. However, the need for an integration over the complicated surface of the Earth and an oblique derivative in the boundary condition make the computation of the entries in Galerkin’s matrix extremely demanding. Therefore, an alternative is considered. For constructing Galerkin’s approximations a function basis is generated by the reproducing kernel of the Hilbert space of functions that are harmonic outside an ellipsoid. Obviously, the method of successive approximations is then applied to account for corrections due to the departure of the real boundary from the ellipsoid and due to the obliqueness of the derivative in the boundary condition. The explanations concerning the construction and computation of the reproducing kernel are given more space. Ellipsoidal harmonics, series summation techniques, hypergeometric functions and elliptic integrals come into play as necessary tools. Finally, the convergence of the successive approximations is analyzed and tested.
- The discussion starts with a general review of iteration concepts as applied for solving BVPs in gravity field studies. The subsequent explanations rest on the weak formulation of the problems. This enables a natural transition to an interpretation of the solution in terms of function bases. However, the need for an integration over the complicated surface of the Earth and an oblique derivative in the boundary condition make the computation of the entries in Galerkin’s matrix extremely demanding. Therefore, an alternative is considered. For constructing Galerkin’s approximations a function basis is generated by the reproducing kernel of the Hilbert space of functions that are harmonic outside an ellipsoid. Obviously, the method of successive approximations is then applied to account for corrections due to the departure of the real boundary from the ellipsoid and due to the obliqueness of the derivative in the boundary condition. The explanations concerning the construction and computation of the reproducing kernel are given more space. Ellipsoidal harmonics, series summation techniques, hypergeometric functions and elliptic integrals come into play as necessary tools. Finally, the convergence of the successive approximations is analyzed and tested. (en)
|
| Title
| - Reproducing Kernel Hilbert Space for the Exterior of an Ellipsoid and the Method of Successive Approximations in Solving GBVPs
- Reproducing Kernel Hilbert Space for the Exterior of an Ellipsoid and the Method of Successive Approximations in Solving GBVPs (en)
|
| skos:prefLabel
| - Reproducing Kernel Hilbert Space for the Exterior of an Ellipsoid and the Method of Successive Approximations in Solving GBVPs
- Reproducing Kernel Hilbert Space for the Exterior of an Ellipsoid and the Method of Successive Approximations in Solving GBVPs (en)
|
| skos:notation
| - RIV/00025615:_____/13:#0001898!RIV14-MSM-00025615
|
| http://linked.open...avai/predkladatel
| |
| http://linked.open...avai/riv/aktivita
| |
| http://linked.open...avai/riv/aktivity
| |
| http://linked.open...vai/riv/dodaniDat
| |
| http://linked.open...aciTvurceVysledku
| |
| http://linked.open.../riv/druhVysledku
| |
| http://linked.open...iv/duvernostUdaju
| |
| http://linked.open...titaPredkladatele
| |
| http://linked.open...dnocenehoVysledku
| |
| http://linked.open...ai/riv/idVysledku
| - RIV/00025615:_____/13:#0001898
|
| http://linked.open...riv/jazykVysledku
| |
| http://linked.open.../riv/klicovaSlova
| - Earth's gravity field; geodetic boundary value problems; vartiational and classical solution; reproducing kernels; elliptic integrals (en)
|
| http://linked.open.../riv/klicoveSlovo
| |
| http://linked.open...i/riv/kodPristupu
| |
| http://linked.open...ontrolniKodProRIV
| |
| http://linked.open...i/riv/mistoVydani
| |
| http://linked.open...telVyzkumneZpravy
| - International Association of Geodesy
|
| http://linked.open...in/vavai/riv/obor
| |
| http://linked.open...ichTvurcuVysledku
| |
| http://linked.open...cetTvurcuVysledku
| |
| http://linked.open...vavai/riv/projekt
| |
| http://linked.open...UplatneniVysledku
| |
| http://linked.open...iv/tvurceVysledku
| - Holota, Petr
- Nesvadba, Otakar
|
![[RDF Data]](/fct/images/sw-rdf-blue.png)
![[cxml]](/fct/images/cxml_doc.png)
![[csv]](/fct/images/csv_doc.png)
![[text]](/fct/images/ntriples_doc.png)
![[turtle]](/fct/images/n3turtle_doc.png)
![[ld+json]](/fct/images/jsonld_doc.png)
![[rdf+json]](/fct/images/json_doc.png)
![[rdf+xml]](/fct/images/xml_doc.png)
![[atom+xml]](/fct/images/atom_doc.png)
![[html]](/fct/images/html_doc.png)