Geodesic metrics for RBF approximation of some physical quantities measured on sphere

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985840%3A_____%2F24%3A00599934" target="_blank" >RIV/67985840:_____/24:00599934 - isvavai.cz</a>

Výsledek na webu

<a href="https://doi.org/10.21136/AM.2024.0051-24" target="_blank" >https://doi.org/10.21136/AM.2024.0051-24</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.21136/AM.2024.0051-24" target="_blank" >10.21136/AM.2024.0051-24</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Geodesic metrics for RBF approximation of some physical quantities measured on sphere

Popis výsledku v původním jazyce

The radial basis function (RBF) approximation is a rapidly developing field of mathematics. In the paper, we are concerned with the measurement of scalar physical quantities at nodes on sphere in the 3D Euclidean space and the spherical RBF interpolation of the data acquired. We employ a multiquadric as the radial basis function and the corresponding trend is a polynomial of degree 2 considered in Cartesian coordinates. Attention is paid to geodesic metrics that define the distance of two points on a sphere. The choice of a particular geodesic metric function is an important part of the construction of interpolation formula. We show the existence of an interpolation formula of the type considered. The approximation formulas of this type can be useful in the interpretation of measurements of various physical quantities. We present an example concerned with the sampling of anisotropy of magnetic susceptibility having extensive applications in geosciences and demonstrate the advantages and drawbacks of the formulas chosen, in particular the strong dependence of interpolation results on condition number of the matrix of the system considered and on round-off errors in general.

Název v anglickém jazyce

Geodesic metrics for RBF approximation of some physical quantities measured on sphere

Popis výsledku anglicky

The radial basis function (RBF) approximation is a rapidly developing field of mathematics. In the paper, we are concerned with the measurement of scalar physical quantities at nodes on sphere in the 3D Euclidean space and the spherical RBF interpolation of the data acquired. We employ a multiquadric as the radial basis function and the corresponding trend is a polynomial of degree 2 considered in Cartesian coordinates. Attention is paid to geodesic metrics that define the distance of two points on a sphere. The choice of a particular geodesic metric function is an important part of the construction of interpolation formula. We show the existence of an interpolation formula of the type considered. The approximation formulas of this type can be useful in the interpretation of measurements of various physical quantities. We present an example concerned with the sampling of anisotropy of magnetic susceptibility having extensive applications in geosciences and demonstrate the advantages and drawbacks of the formulas chosen, in particular the strong dependence of interpolation results on condition number of the matrix of the system considered and on round-off errors in general.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10101 - Pure mathematics

Projekt

—

Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2024

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

Applications of Mathematics

ISSN

0862-7940

e-ISSN

1572-9109

Svazek periodika

69

Číslo periodika v rámci svazku

5

Stát vydavatele periodika

DE - Spolková republika Německo

Počet stran výsledku

12

Strana od-do

621-632

Kód UT WoS článku

001306175200001

EID výsledku v databázi Scopus

2-s2.0-85203197509