A Minimum Norm Interpolation Method for Determining the Displacement Field of a Homogeneous Isotropic Elastic Body from Discrete Data

Freeden, Willi; Gervens, T.; Mason, J. C.

doi:10.1093/imamat/44.1.55

Cited by 17 publications

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“…[7,9,24,25]. They have also been proved to be a powerful tool for the solution of boundary value problems with discretely given data, even for non spherical boundaries (see [8,10,22]). The advantage of spherical spline interpolation lies mainly in two points: (i) It is applicable (under mild conditions) to all scattered data situations on the sphere.…”

Section: Introductionmentioning

confidence: 99%

Locally Supported Kernels for Spherical Spline Interpolation

Schreiner

1997

Journal of Approximation Theory

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By the use of locally supported basis functions for spherical spline interpolation the applicability of this approximation method is extended, since the resulting interpolation matrix is sparse and thus efficient solvers can be used. In this paper we study locally supported kernels in detail. Investigations on the Legendre coefficients allow a characterization of the underlying Hilbert space structure. We show how spherical spline interpolation with polynomial precision can be managed with locally supported kernels, thus giving the possibility to combine approximation techniques based on spherical harmonic expansions with those based on locally supported kernels.1997 Academic Press

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Section: Introductionmentioning

confidence: 99%

Locally Supported Kernels for Spherical Spline Interpolation

Schreiner

1997

Journal of Approximation Theory

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Vector spherical spline interpolation—basic theory and computational aspects

Freeden

Gervens

1993

Math Methods in App Sciences

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Communicated by H. NeunzertVector spherical interpolation is discussed from both the theoretical and computational points of view. The theory of vector spherical harmonics is an essential tool. An estimate is given for the absolute error of the interpolation process; an efficient algorithm is developed for the computation of a vector spherical interpolant. The displacement boundary value problem of determining the elastic field from a finite number of discretely given displacement vectors is solved by the use of vector splines. IntroductionNumerous papers concerned with the scalar interpolation theory of spherical splines have appeared in the last decade. Scalar spherical splines (SSS) have been analyzed in depth both in their theoretical and computational aspects (cf., e.g., [8-10, 12,213 and the references therein) and have been found to be natural generalizations of polynomials, that is spherical harmonics, having desirable characteristics as interpolating functions; SSS can be recommended for the numerical solution of various interpolation and best-approximation problems in geosciences. In particular, S S S are best suited for the macromodelling and micromodelling of the Earth's gravitational field from discretely given data on the Earth's suface (cf., e.g., [4,5, 10, 16, 171). Moreover, based on the ideas of the scalar theory, a successful application of spherical splines has been given to the analysis of meteorological data In this paper we establish a general vectorial concept of spherical spline interpolation. More explicitly, our focus will be on the determination of a spherical vector field from discretely given normal and tangential components. It turns out that interpolation by vector spherical splines (VSS) essentially amounts to solving a well-posed (cf. [22]).

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Introduction: Geomathematical Motivation

Freeden

Gutting

2012

Special Functions of Mathematical (Geo-)Physics

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A Minimum Norm Interpolation Method for Determining the Displacement Field of a Homogeneous Isotropic Elastic Body from Discrete Data

Cited by 17 publications

References 0 publications

Locally Supported Kernels for Spherical Spline Interpolation

Locally Supported Kernels for Spherical Spline Interpolation

Vector spherical spline interpolation—basic theory and computational aspects

Introduction: Geomathematical Motivation

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