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ENO reconstruction and ENO interpolation are stable
 FOUND COMPUT MATH
, 2012
"... ... are stable in the sense that the jump of the reconstructed ENO point values at each cell interface has the same sign as the jump of the underlying cell averages across that interface. Moreover, we prove that the size of these jumps after reconstruction relative to the jump of the underlying cell ..."
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Cited by 4 (3 self)
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cell averages is bounded. Similar sign properties and the boundedness of the jumps hold for the ENO interpolation procedure. These estimates, which are shown to hold for ENO reconstruction and interpolation of arbitrary order of accuracy and on nonuniform meshes, indicate a remarkable rigidity
Efficient Implementation of Weighted ENO Schemes
, 1995
"... In this paper, we further analyze, test, modify and improve the high order WENO (weighted essentially nonoscillatory) finite difference schemes of Liu, Osher and Chan [9]. It was shown by Liu et al. that WENO schemes constructed from the r th order (in L¹ norm) ENO schemes are (r +1) th order accur ..."
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Cited by 412 (38 self)
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In this paper, we further analyze, test, modify and improve the high order WENO (weighted essentially nonoscillatory) finite difference schemes of Liu, Osher and Chan [9]. It was shown by Liu et al. that WENO schemes constructed from the r th order (in L¹ norm) ENO schemes are (r +1) th order
Global analyses of sea surface temperature, sea ice, and night marine air temperature since the late Nineteenth Century
 J. GEOPHYSICAL RESEARCH
, 2003
"... ... data set, HadISST1, and the nighttime marine air temperature (NMAT) data set, HadMAT1. HadISST1 replaces the global sea ice and sea surface temperature (GISST) data sets and is a unique combination of monthly globally complete fields of SST and sea ice concentration on a 1 ° latitudelongitude g ..."
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Cited by 539 (4 self)
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interpolation procedure, followed by superposition of qualityimproved gridded observations onto the reconstructions to restore local detail. The sea ice fields are made more homogeneous by compensating satellite microwavebased sea ice concentrations for the impact of surface melt effects on retrievals
ReTiling Polygonal Surfaces
 Computer Graphics
, 1992
"... This paper presents an automatic method of creating surface models at several levels of detail from an original polygonal description of a given object. Representing models at various levels of detail is important for achieving high frame rates in interactive graphics applications and also for speed ..."
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Cited by 445 (3 self)
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curvature and 3) a method of smoothly interpolating between models that represent the same object at different levels of detail. The key notion in the retiling procedure is the creation of an intermediate model called the mutual tessellation of a surface that contains both the vertices from the original
Weighted Essentially NonOscillatory Schemes
, 1994
"... In this paper we introduce a new version of ENO (Essentially NonOscillatory) shockcapturing schemes which we call Weighted ENO. The main new idea is that, instead of choosing the "smoothest" stencil to pick one interpolating polynomial for the ENO reconstruction, we use a convex combinati ..."
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Cited by 326 (8 self)
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In this paper we introduce a new version of ENO (Essentially NonOscillatory) shockcapturing schemes which we call Weighted ENO. The main new idea is that, instead of choosing the "smoothest" stencil to pick one interpolating polynomial for the ENO reconstruction, we use a convex
Sampling—50 years after Shannon
 Proceedings of the IEEE
, 2000
"... This paper presents an account of the current state of sampling, 50 years after Shannon’s formulation of the sampling theorem. The emphasis is on regular sampling, where the grid is uniform. This topic has benefited from a strong research revival during the past few years, thanks in part to the math ..."
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Cited by 339 (27 self)
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to the mathematical connections that were made with wavelet theory. To introduce the reader to the modern, Hilbertspace formulation, we reinterpret Shannon’s sampling procedure as an orthogonal projection onto the subspace of bandlimited functions. We then extend the standard sampling paradigm for a representation
Essentially nonoscillatory and weighted essentially nonoscillatory schemes for hyperbolic conservation laws
, 1998
"... In these lecture notes we describe the construction, analysis, and application of ENO (Essentially NonOscillatory) and WENO (Weighted Essentially NonOscillatory) schemes for hyperbolic conservation laws and related HamiltonJacobi equations. ENO and WENO schemes are high order accurate nite di ere ..."
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Cited by 270 (26 self)
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erence schemes designed for problems with piecewise smooth solutions containing discontinuities. The key idea lies at the approximation level, where a nonlinear adaptive procedure is used to automatically choose the locally smoothest stencil, hence avoiding crossing discontinuities in the interpolation
Quasilinear subdivision schemes with applications to ENO interpolation
 ACHA
, 2001
"... We analyze the convergence and smoothness of certain class of nonlinear subdivision schemes. We study the stability properties of these schemes and apply this analysis to the speci c class based on ENO and weightedENO interpolation techniques. Our interest in these techniques is motivated by their ..."
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Cited by 26 (6 self)
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We analyze the convergence and smoothness of certain class of nonlinear subdivision schemes. We study the stability properties of these schemes and apply this analysis to the speci c class based on ENO and weightedENO interpolation techniques. Our interest in these techniques is motivated
StyleBased Inverse Kinematics
, 2004
"... This paper presents an inverse kinematics system based on a learned model of human poses. Given a set of constraints, our system can produce the most likely pose satisfying those constraints, in realtime. Training the model on different input data leads to different styles of IK. The model is repres ..."
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Cited by 211 (8 self)
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Variable Model. The parameters of the model are all learned automatically; no manual tuning is required for the learning component of the system. We additionally describe a novel procedure for interpolating between styles. Our stylebased
Robust Solutions To LeastSquares Problems With Uncertain Data
, 1997
"... . We consider leastsquares problems where the coefficient matrices A; b are unknownbutbounded. We minimize the worstcase residual error using (convex) secondorder cone programming, yielding an algorithm with complexity similar to one singular value decomposition of A. The method can be interpret ..."
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Cited by 205 (14 self)
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be interpreted as a Tikhonov regularization procedure, with the advantage that it provides an exact bound on the robustness of solution, and a rigorous way to compute the regularization parameter. When the perturbation has a known (e.g., Toeplitz) structure, the same problem can be solved in polynomial
Results 1  10
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1,570