TY - INPR
A1 - Kammann, Paula
A1 - Michel, Volker
T1 - Time-Dependent Cauchy-Navier Splines and their Application to Seismic Wave Front Propagation
N2 - In this paper a known orthonormal system of time- and space-dependent functions, that were derived out of the Cauchy-Navier equation for elastodynamic phenomena, is used to construct reproducing kernel Hilbert spaces. After choosing one of the spaces the corresponding kernel is used to define a function system that serves as a basis for a spline space. We show that under certain conditions there exists a unique interpolating or approximating, respectively, spline in this space with respect to given samples of an unknown function. The name "spline" here refers to its property of minimising a norm among all interpolating functions. Moreover, a convergence theorem and an error estimate relative to the point grid density are derived. As numerical example we investigate the propagation of seismic waves.
T3 - Schriften zur Funktionalanalysis und Geomathematik - 26
KW - Spline
KW - Sphäre
KW - Elastizität
KW - Seismische Welle
KW - Zeitabhängigkeit
KW - Approximation
KW - reproduzierender Kern
KW - Cauchy-Navier-Gleichung
KW - reproducing kernel
KW - spline
KW - sphere
KW - seismic wave
KW - Cauchy-Navier equation
Y1 - 2006
UR - https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1760
UR - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:hbz:386-kluedo-14373
ER -