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327,076
Bounds for the Range of a Bivariate Polynomial over a Triangle
 Reliable Computing
, 1998
"... this paper we consider the following PROBLEM. Let a bivariate polynomial p(x; y) = ..."
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Cited by 5 (3 self)
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this paper we consider the following PROBLEM. Let a bivariate polynomial p(x; y) =
Error Bounds for Minimal Energy Bivariate Polynomial Splines
 Numer. Math
, 2001
"... We derive error bounds for bivariate spline interpolants which are calculated by minimizing certain natural energy norms. x1. ..."
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Cited by 14 (13 self)
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We derive error bounds for bivariate spline interpolants which are calculated by minimizing certain natural energy norms. x1.
Network Centric Warfare: Developing and Leveraging Information Superiority
 Command and Control Research Program (CCRP), US DoD
, 2000
"... the mission of improving DoD’s understanding of the national security implications of the Information Age. Focusing upon improving both the state of the art and the state of the practice of command and control, the CCRP helps DoD take full advantage of the opportunities afforded by emerging technolo ..."
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Cited by 308 (5 self)
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technologies. The CCRP pursues a broad program of research and analysis in information superiority, information operations, command and control theory, and associated operational concepts that enable us to leverage shared awareness to improve the effectiveness and efficiency of assigned missions. An important
On the Approximation Power of Bivariate Splines
 Advances in Comp. Math. 9
, 1996
"... . We show how to construct stable quasiinterpolation schemes in the bivariate spline spaces S r d (4) with d 3r+2 which achieve optimal approximation order. In addition to treating the usual max norm, we also give results in the Lp norms, and show that the methods also approximate derivatives to ..."
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Cited by 59 (36 self)
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to optimal order. We pay special attention to the approximation constants, and show that they depend only on the the smallest angle in the underlying triangulation and the nature of the boundary of the domain. AMS(MOS) Subject Classifications: 41A15, 41A63, 41A25, 65D10 Keywords and phrases: Bivariate
Bounds on Projections onto Bivariate Polynomial Spline Spaces with Stable Bases
 Constr. Approx
, 2002
"... . We derive L1 bounds for norms of projections onto bivariate polynomial spline spaces on regular triangulations with stable local bases. We then apply this result to derive error bounds for best L 2  and ` 2 approximation by splines on quasiuniform triangulations. x1. Introduction Let X ` L1(\O ..."
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Cited by 19 (3 self)
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:2) Suppose S ` X is a linear space of polynomial splines (bivariate piecewise polynomials) defined on a regular triangulation 4 of\Omega (two triangles intersect only at a common vertex or along a common edge). We assume that S is a Hilbert space with respect to h\Delta; \Deltai. Let P : X
disk and triangle
, 2010
"... Leastsquares polynomial approximation on weakly admissible meshes: ..."
Bivariate Polynomial Interpolation at the Geronimus Nodes
"... Abstract. We consider a class of orthogonal polynomials that satisfy a threeterm recurrence formula with constant coefficients. This class contains the Geronimus class and, in particular, all four kinds of the Chebyshev polynomials. There are alternation points for each of these orthogonal polynomia ..."
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the reproducing kernel) for bivariate Lagrange polynomials for the Geronimus nodes and we apply this to obtain a bivariate interpolation theorem and a cubature formula. These theorems are a consequence of a surprisingly elementary connection between Lagrange polynomials, interpolation formulas and cubature
A Tool Kit for Finding Small Roots of Bivariate Polynomials over the Integers
 Advances in Cryptology – Eurocrypt 2005, Lecture Notes in Computer Science
, 2005
"... Abstract. We present a new and flexible formulation of Coppersmith’s method for finding small solutions of bivariate polynomials p(x, y) over the integers. Our approach allows to maximize the bound on the solutions of p(x, y) in a purely combinatorial way. We give various construction rules for diff ..."
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Cited by 14 (1 self)
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Abstract. We present a new and flexible formulation of Coppersmith’s method for finding small solutions of bivariate polynomials p(x, y) over the integers. Our approach allows to maximize the bound on the solutions of p(x, y) in a purely combinatorial way. We give various construction rules
Results 1  10
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327,076