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Approximation by Piecewise Polynomials on Voronoi Tessellation
"... We propose a novel method to approximate a function on 2D domain by piecewise polynomials. The Voronoi tessellation is used as a partition of the domain, on which the best fitting polynomials in L2 metric are constructed. Our method optimizes the domain partition and the fitting polynomials simultan ..."
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We propose a novel method to approximate a function on 2D domain by piecewise polynomials. The Voronoi tessellation is used as a partition of the domain, on which the best fitting polynomials in L2 metric are constructed. Our method optimizes the domain partition and the fitting polynomials
Adaptive and anisotropic piecewise polynomial approximation
, 2011
"... We survey the main results of approximation theory for adaptive piecewise polynomial functions. In such methods, the partition on which the piecewise polynomial approximation is defined is not fixed in advance, but adapted to the given function f which is approximated. We focus our discussion on (i) ..."
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Cited by 4 (2 self)
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We survey the main results of approximation theory for adaptive piecewise polynomial functions. In such methods, the partition on which the piecewise polynomial approximation is defined is not fixed in advance, but adapted to the given function f which is approximated. We focus our discussion on (i
Piecewise Polynomial Representations of Genomic Tracks
, 2012
"... Genomic data from microarray and sequencing projects consist of associations of measured values to chromosomal coordinates. These associations can be thought of as functions in one dimension and can thus be stored, analyzed, and interpreted as piecewisepolynomial curves. We present a general frame ..."
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Genomic data from microarray and sequencing projects consist of associations of measured values to chromosomal coordinates. These associations can be thought of as functions in one dimension and can thus be stored, analyzed, and interpreted as piecewisepolynomial curves. We present a general
Piecewise polynomial nonlinear model reduction
 in Design Automation Conference
"... We present a novel, general approach towards modelorder reduction (MOR) of nonlinear systems that combines good global and local approximation properties. The nonlinear system is first approximated as piecewise polynomials over a number of regions, following which each region is reduced via pol ..."
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Cited by 33 (3 self)
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We present a novel, general approach towards modelorder reduction (MOR) of nonlinear systems that combines good global and local approximation properties. The nonlinear system is first approximated as piecewise polynomials over a number of regions, following which each region is reduced via
EXTENDING PIECEWISE POLYNOMIAL FUNCTIONS IN TWO VARIABLES
"... Abstract. We study the extendibility of piecewise polynomial functions defined on closed subsets of R2. The compact subsets on which every piecewise polynomial function is extensible can be characterized in terms of quasiconvexity if they are definable in an ominimal expansion of the real field. Ev ..."
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Abstract. We study the extendibility of piecewise polynomial functions defined on closed subsets of R2. The compact subsets on which every piecewise polynomial function is extensible can be characterized in terms of quasiconvexity if they are definable in an ominimal expansion of the real field
Nonlinear piecewise polynomial approximation beyond Besov spaces
 Appl. Comput. Harmonic Anal
"... We study nonlinear nterm approximation in Lp(R2) (0 < p < ∞) from Courant elements or (discontinuous) piecewise polynomials generated by multilevel nested triangulations of R2 which allow arbitrarily sharp angles. To characterize the rate of approximation we introduce and develop three famili ..."
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Cited by 32 (12 self)
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We study nonlinear nterm approximation in Lp(R2) (0 < p < ∞) from Courant elements or (discontinuous) piecewise polynomials generated by multilevel nested triangulations of R2 which allow arbitrarily sharp angles. To characterize the rate of approximation we introduce and develop three
Discrete Sobolev and Poincaré inequalities for piecewise polynomial functions
 ELECTRON TRANS. NUMER. ANAL
, 2004
"... Discrete Sobolev and Poincaré inequalities are derived for piecewise polynomial functions on two dimensional domains. These inequalities can be applied to classical nonconforming finite element methods and discontinuous Galerkin methods. ..."
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Cited by 3 (1 self)
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Discrete Sobolev and Poincaré inequalities are derived for piecewise polynomial functions on two dimensional domains. These inequalities can be applied to classical nonconforming finite element methods and discontinuous Galerkin methods.
Fat Points, Inverse Systems, and Piecewise Polynomial Functions
, 2004
"... We explore the connection between ideals of fat points (which correspond to subschemes of P n obtained by intersecting (mixed) powers of ideals of points), and piecewise polynomial functions (splines) on a ddimensional simplicial complex # embedded in R^d. Using the ..."
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Cited by 21 (7 self)
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We explore the connection between ideals of fat points (which correspond to subschemes of P n obtained by intersecting (mixed) powers of ideals of points), and piecewise polynomial functions (splines) on a ddimensional simplicial complex # embedded in R^d. Using the
Computing Moments of Piecewise Polynomial Surfaces
, 1997
"... Combining the advantages of a lowdegree polynomial surface representation with Gauss' divergence theorem allows efficient and exact calculation of the moments of objects enclosed by a freeform surface. Volume, center of mass and the inertia tensor can be computed in seconds even for complex o ..."
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Cited by 2 (1 self)
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Combining the advantages of a lowdegree polynomial surface representation with Gauss' divergence theorem allows efficient and exact calculation of the moments of objects enclosed by a freeform surface. Volume, center of mass and the inertia tensor can be computed in seconds even for complex
Results 11  20
of
1,335