127 research outputs found
Two-dimensional interpolation using a cell-based searching procedure
In this paper we present an efficient algorithm for bivariate interpolation,
which is based on the use of the partition of unity method for constructing a
global interpolant. It is obtained by combining local radial basis function
interpolants with locally supported weight functions. In particular, this
interpolation scheme is characterized by the construction of a suitable
partition of the domain in cells so that the cell structure strictly depends on
the dimension of its subdomains. This fact allows us to construct an efficient
cell-based searching procedure, which provides a significant reduction of CPU
times. Complexity analysis and numerical results show such improvements on the
algorithm performances
A trivariate interpolation algorithm using a cube-partition searching procedure
In this paper we propose a fast algorithm for trivariate interpolation, which
is based on the partition of unity method for constructing a global interpolant
by blending local radial basis function interpolants and using locally
supported weight functions. The partition of unity algorithm is efficiently
implemented and optimized by connecting the method with an effective
cube-partition searching procedure. More precisely, we construct a cube
structure, which partitions the domain and strictly depends on the size of its
subdomains, so that the new searching procedure and, accordingly, the resulting
algorithm enable us to efficiently deal with a large number of nodes.
Complexity analysis and numerical experiments show high efficiency and accuracy
of the proposed interpolation algorithm
Two and Three Dimensional Partition of Unity Interpolation by Product-Type Functions
In this paper we analyze the behavior of product-type radial basis functions (RBFs) and splines, which are used in a partition of unity interpolation scheme as local approximants. In particular, we deal with the case of bivariate and trivariate interpolation on a relatively large number of scattered data points. Thus, we propose the local use of compactly supported RBF and spline interpolants, which take advantage of being expressible in the multivariate setting as a product of univariate functions. Numerical experiments show good accuracy and stability of the partition of unity method combined with these product-type interpolants, comparing it with the one obtained by replacing compactly supported RBFs and splines with Gaussians
Fast and flexible interpolation via PUM with applications in population dynamics
In this paper the Partition of Unity Method (PUM) is efficiently performed
using Radial Basis Functions (RBFs) as local approximants. In particular, we
present a new space-partitioning data structure extremely useful in
applications because of its independence from the problem geometry. Moreover,
we study, in the context of wild herbivores in forests, an application of such
algorithm. This investigation shows that the ecosystem of the considered
natural park is in a very delicate situation, for which the animal population
could become extinguished. The determination of the so-called sensitivity
surfaces, obtained with the new fast and flexible interpolation tool, indicates
some possible preventive measures to the park administrators
Local interpolation schemes for landmark-based image registration: a comparison
In this paper we focus, from a mathematical point of view, on properties and
performances of some local interpolation schemes for landmark-based image
registration. Precisely, we consider modified Shepard's interpolants,
Wendland's functions, and Lobachevsky splines. They are quite unlike each
other, but all of them are compactly supported and enjoy interesting
theoretical and computational properties. In particular, we point out some
unusual forms of the considered functions. Finally, detailed numerical
comparisons are given, considering also Gaussians and thin plate splines, which
are really globally supported but widely used in applications
Hermite-Birkhoff Interpolation on Arbitrarily Distributed Data on the Sphere and Other Manifolds
We consider the problem of interpolating a function given on scattered points
using Hermite-Birkhoff formulas on the sphere and other manifolds. We express
each proposed interpolant as a linear combination of basis functions, the
combination coefficients being incomplete Taylor expansions of the interpolated
function at the interpolation points. The basis functions have the following
features: (i) depend on the geodesic distance; (ii) are orthonormal with
respect to the point-evaluation functionals; and (iii) have all derivatives
equal zero up to a certain order at the interpolation points. Moreover, the
construction of such interpolants, which belong to the class of partition of
unity methods, takes advantage of not requiring any solution of linear systems
Partition of Unity Interpolation on Multivariate Convex Domains
In this paper we present a new algorithm for multivariate interpolation of
scattered data sets lying in convex domains \Omega \subseteq \RR^N, for any
. To organize the points in a multidimensional space, we build a
-tree space-partitioning data structure, which is used to efficiently apply
a partition of unity interpolant. This global scheme is combined with local
radial basis function approximants and compactly supported weight functions. A
detailed description of the algorithm for convex domains and a complexity
analysis of the computational procedures are also considered. Several numerical
experiments show the performances of the interpolation algorithm on various
sets of Halton data points contained in , where can be any
convex domain like a 2D polygon or a 3D polyhedron
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