W. Freeden, T. Gervens, and M. Schneider. Constructive approximation on the sphere: with applications to geomathematics. Clarendon Press, Oxford, 1998. Home/Search Document Not in Database Summary Related Articles Check |
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On the Approximation Order of Splines on Spherical.. - Neamtu, Schumaker (Correct)
....When considering functions on the entire sphere S, i.e. when Omega = S, then one possibility is to define a seminorm that annihilates all spherical polynomials of a given degree d in terms of the well known Laplace Beltrami operator 4 . Namely, the following operator, used extensively in [10,16], has Pi d (S) as its null space: 4 d : ae (4 0 ) 4 2 ) Delta Delta Delta (4 d ) d even, 4 1 ) 4 3 ) Delta Delta Delta (4 d ) d odd, 3:4) where k : k(k 1) k 2 ZZ . Unfortunately, 4 d is not suitable for working with functions on ....
Freeden, W., T. Gervens, and M. Schreiner, Constructive Approximation on the Sphere with Applications to Geomathematics, Oxford Univ. Press, Oxford, 1998.
Splines on Surfaces - Neamtu (2001) (1 citation) (Correct)
....so called variational methods have their counterparts on the sphere. Strictly speaking, variational methods belong to the previous subsection since the kernels 20 associated with the extremal problem also happen to be radially symmetric. The methods have been frequently used in geosciences, see [29 31,33,75 77]. Another popular method, often applied in meteorology, is the classical spectral method, which uses spherical harmonics of high degrees to approximate functions on the sphere (which corresponds to using ordinary polynomials in the plane) see [44] 3.4. Distance Weighting Methods This class of ....
W. Freeden, T. Gervens, and M. Schreiner, Constructive Approximation on the Sphere With Applications to Geomathematics, Oxford University Press, Oxford, 1998.
Moving Least Squares Approximation on the Sphere - Wendland (2001) (Correct)
....in general. Over the last years several approaches were made to reconstruct a continuous function on the sphere from a finite number of discrete data (see [4] for a recent overview) One possibility is based on the theory of radial basis functions. Much work in this direction was done by [5,6,9,15] and this list is far from being complete. Even if this approach allows to use scattered data for the reconstruction process, the computation of the approximating function needs the solution of a full N Theta N linear system where N denotes the number of centers, and is intolerably expensive ....
Freeden, W., T. Gervens, and M. Schreiner, Constructive Approximation on the Sphere with Applications to Geomathematics, Clarendon Press, Oxford, 1998.
Polynomial Frames on the Sphere - Mhaskar, Narcowich, Ward, Prestin (1 citation) (Correct)
.... low frequency components with the hope of further understanding various properties of the function, for example location of singularities. The standard wavelet paradigm of constructing spaces based on an increasing chain of lattices does not apply to this situation. Nevertheless, many authors [2, 3, 8, 23, 28] have derived various nonstationary constructions of wavelets or frames on the sphere. Such constructions fall roughly into three categories: continuous wavelet transforms (CWT) discrete wavelets or frames and biorthogonal wavelets using lifting techniques. Each approach seems to have its ....
W. Freeden, T. Gervens, and M. Schreiner, Constructive Approximation on the Sphere: with Applications to Geomathematics, Clarendon Press, Oxford, 1998.
Error Bounds for Solving Pseudodifferential Equations on.. - Morton, Neamtu (1999) (1 citation) (Correct)
....approximation order, sphere, positive definite function, radial basis function. x1. Introduction Data fitting and solving differential and integral equations on the sphere are areas of growing interest with applications to physical geodesy, potential theory, oceanography, and meteorology [6,10]. As more and more satellites are being launched into space, the acquisition of global data is becoming more important and more widespread, and the demand for spherical data processing and solving problems of a global nature is increasing. In this paper we investigate the solution of ....
....geodesic distance of p from q, the function (p; Delta) is radially symmetric with respect to the point p. For this reason (p; Delta) is often called a spherical radial basis function. Differential or, more generally, pseudodifferential equations arise in many areas of earth sciences (see e.g. [10,25] for many important examples) Given a pseudodifferential operator L and a spherical function f , our objective in this paper is to discuss approximate solutions of the equation Lu = f: In order that this equation may be uniquely solvable, side conditions will be imposed of the form flu = d fl ....
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Freeden, W., T. Gervens, and M. Schreiner, Constructive Approximation on the Sphere With Applications to Geomathematics, Oxford University Press, Oxford, 1998.
Orthogonal Non-Bandlimited Wavelets on the Sphere - Freeden, Michel Self-citation (Freeden) (Correct)
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W. Freeden, T. Gervens and M. Schreiner (1998): Constructive Approximation on the Sphere - With Applications to Geomathematics, Oxford University Press, Oxford.
Orthogonal Non-Bandlimited Wavelets on the Sphere - Freeden, Michel Self-citation (Freeden) (Correct)
No context found.
W. Freeden, T. Gervens and M. Schreiner (1998): Constructive Approximation on the Sphere - With Applications to Geomathematics, Oxford University Press, Oxford.
Optimally Space-Localized Band-Limited Wavelets on S^q-1 - Fernandez (2005) (Correct)
No context found.
W. Freeden, T. Gervens, and M. Schneider. Constructive approximation on the sphere: with applications to geomathematics. Clarendon Press, Oxford, 1998.
Interpolatory Band-limited Wavelet Bases on the Sphere - Fernandez, Prestin (2005) (Correct)
No context found.
W. Freeden, T. Gervens, and M. Schneider. Constructive approximation on the sphere: with applications to geomathematics. Clarendon Press, Oxford, 1998.
Wavelets on the 2-Sphere: A Group-Theoretical Approach - Antoine, Vandergheynst (1999) (1 citation) (Correct)
No context found.
W. Freeden, M. Schreiner, and T. Gervens, "Constructive Approximation on the Sphere, with Applications to Geomathematics," Clarendon Press, Oxford, 1997.
Stereographic Frames of Wavelets on the Sphere - Bogdanova And Vandergheynst (2004) (Correct)
No context found.
W. Freeden, T. Gervens, M. Schreiner. Constructive Approximations on the Sphere: With applications to Geomathematics. Clarendon Press, Oxford 1998. 15
Wavelet Representation of Diffraction Pole Figures - Schaeben, Prestin, Potts (Correct)
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Freeden, W., Gervens, T., Schreiner, M., Constructive Approximation on the Sphere: with Applications to Geomathematics, Clarendon Press: Oxford, 1998.
Multiresolution on the Sphere - Conrad, Prestin (Correct)
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W. Freeden, T. Gervens and M. Schreiner. Constructive Approximation on the Sphere: with Applications to Geomathematics. Clarendon Press, Oxford, 1998.
Spherical Wavelets with an application in preferred.. - Schaeben, Potts, Prestin (2001) (Correct)
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Freeden, W., Gervens, T., and Schreiner, M., 1998, Constructive Approximation on the Sphere with Applications to Geomathematics; Clarendon Press
Spatio-temporal Pattern Formation on Spherical Surfaces: .. - Chaplain, Ganesh, Graham (1 citation) (Correct)
No context found.
W. Freeden, T. Gervens and M. Schreiner, Constructive Approximation on the Sphere with Applications to Geomathematics, Clarendon Press, Oxford, 1998.
Spatio-temporal Pattern Formation on Spherical Surfaces: .. - Chaplain, Ganesh, Graham (1 citation) (Correct)
No context found.
W. Freeden, T. Gervens and M. Schreiner, Constructive Approximation on the Sphere with Applications to Geomathematics, Clarendon Press, Oxford, 1998.
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