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7,388
Integrated Multiquadric Radial Basis Function Approximation Methods
"... Abstract|Promising numerical results using once and twice integrated radial basis functions have been recently presented. In this work we investigate the integrated radial basis function (IRBF) concept in greater detail, connect to the existing RBF theory, and make conjectures about the properties o ..."
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Cited by 16 (6 self)
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Abstract|Promising numerical results using once and twice integrated radial basis functions have been recently presented. In this work we investigate the integrated radial basis function (IRBF) concept in greater detail, connect to the existing RBF theory, and make conjectures about the properties
Computational Aspects of Radial Basis Function Approximation
"... This paper gives an overview on numerical aspects of multivariate interpolation and approximation by radial basis functions. It comments on the correct choice of the basis function. It discusses the reduction of complexity by different methods as well as the problem of ill-conditioning. It is aimed ..."
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Cited by 7 (0 self)
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This paper gives an overview on numerical aspects of multivariate interpolation and approximation by radial basis functions. It comments on the correct choice of the basis function. It discusses the reduction of complexity by different methods as well as the problem of ill-conditioning. It is aimed
Discontinuous Radial Basis Function Approximations for Meshfree Methods
"... Summary. Meshfree methods with discontinuous radial basis functions and their numerical implementation for elastic problems are presented. We study the following radial basis functions: the multiquadratic (MQ), the Gaussian basis functions and the thin-plate basis functions. These radial basis funct ..."
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Summary. Meshfree methods with discontinuous radial basis functions and their numerical implementation for elastic problems are presented. We study the following radial basis functions: the multiquadratic (MQ), the Gaussian basis functions and the thin-plate basis functions. These radial basis
Radial Basis Function Approximation in the Dual Reciprocity Method
- Mathematical and Computer Modelling
, 1994
"... The Dual Reciprocity Method (DRM) is a class of boundary element techniques wherein, the domain integral resulting from the non-homogeneous terms in Poisson type equations is transferred to equivalent boundary integral by using suitable approximation functions. The use of radial basis functions (RBF ..."
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Cited by 2 (2 self)
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The Dual Reciprocity Method (DRM) is a class of boundary element techniques wherein, the domain integral resulting from the non-homogeneous terms in Poisson type equations is transferred to equivalent boundary integral by using suitable approximation functions. The use of radial basis functions
Local radial basis function approximation on the sphere
, 2008
"... In this paper we derive local error estimates for radial basis function interpolation on the unit sphere S2 R3. More precisely, we consider radial basis function interpolation based on data on a (global or lo-cal) point set X S2 for functions in the Sobolev space Hs(S2) with norm k ks, where s> ..."
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Cited by 1 (0 self)
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In this paper we derive local error estimates for radial basis function interpolation on the unit sphere S2 R3. More precisely, we consider radial basis function interpolation based on data on a (global or lo-cal) point set X S2 for functions in the Sobolev space Hs(S2) with norm k ks, where s
Texture Analysis and Radial Basis Function Approximation for IVUS Image Segmentation
"... Abstract: Intravascular ultrasound (IVUS) has become in the last years an important tool in both clinical and research applications. The detection of lumen and media-adventitia borders in IVUS images represents a first necessary step in the utilization of the IVUS data for the 3D reconstruction of h ..."
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Cited by 1 (1 self)
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corresponding contour of interest, based on the results of texture analysis, and a procedure for approximating the initialization results with smooth continuous curves. A multilevel Discrete Wavelet Frames decomposition is used for texture analysis, whereas Radial Basis Function approximation is employed
Radial Basis Function Approximation: From Gridded Centers to Scattered Centers
, 1993
"... The paper studies L1 (IR d )-norm approximations from a space spanned by a discrete set of translates of a basis function OE. Attention here is restricted to functions OE whose Fourier transform is smooth on IR d n0, and has a singularity at the origin. Examples of such basis functions are the t ..."
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Cited by 19 (4 self)
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are the thin-plate splines and the multiquadrics, as well as other types of radial basis functions that are employed in Approximation Theory. The above approximation problem is well-understood in case the set of points \Xi used for translating OE forms a lattice in IR d , and many optimal and quasi
Digital Total Variation filtering as postprocessing for Radial Basis Function Approximation Methods
- Computers and Mathematics with Applications 52
"... Digital total variation filtering is analyzed as a fast, robust, post-processing method for accelerating the convergence of pseudospectral approximations that have been contaminated by Gibbs oscillations. The method, which originated in image processing, can be combined with spectral filters to quic ..."
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Cited by 9 (5 self)
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Digital total variation filtering is analyzed as a fast, robust, post-processing method for accelerating the convergence of pseudospectral approximations that have been contaminated by Gibbs oscillations. The method, which originated in image processing, can be combined with spectral filters
On Gaussian Radial Basis Function Approximations: Interpretation, Extensions, and Learning Strategies
, 2000
"... In this paper we focus on an interpretation of Gaussian radial basis functions (GRBF) which motivates extensions and learning strategies. Specifically, we show that GRBF regression equations naturally result from representing the input-output joint probability density function by a finite mixture of ..."
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Cited by 5 (1 self)
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In this paper we focus on an interpretation of Gaussian radial basis functions (GRBF) which motivates extensions and learning strategies. Specifically, we show that GRBF regression equations naturally result from representing the input-output joint probability density function by a finite mixture
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7,388
