Results 1  10
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142
Polygonization of Implicit Surfaces
, 1988
"... This paper discusses a numerical technique that approximates an implicit surface with a polygonal representation. The implicit function is adaptively sampled as it is surrounded by a spatial partitioning. The partitioning is represented by an octree, which may either converge to the surface or track ..."
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Cited by 373 (3 self)
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This paper discusses a numerical technique that approximates an implicit surface with a polygonal representation. The implicit function is adaptively sampled as it is surrounded by a spatial partitioning. The partitioning is represented by an octree, which may either converge to the surface or track it. A piecewise polygonal representation is derived from the octree.
A Decomposition Approach for Stochastic Reward Net Models
 Perf. Eval
, 1993
"... We present a decomposition approach for the solution of large stochastic reward nets (SRNs) based on the concept of nearindependence. The overall model consists of a set of submodels whose interactions are described by an import graph. Each node of the graph corresponds to a parametric SRN submodel ..."
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Cited by 102 (27 self)
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We present a decomposition approach for the solution of large stochastic reward nets (SRNs) based on the concept of nearindependence. The overall model consists of a set of submodels whose interactions are described by an import graph. Each node of the graph corresponds to a parametric SRN submodel and an arc from submodel A to submodel B corresponds to a parameter value that B must receive from A. The quantities exchanged between submodels are based on only three primitives. The import graph normally contains cycles, so the solution method is based on fixed point iteration. Any SRN containing one or more of the nearlyindependent structures we present, commonly encountered in practice, can be analyzed using our approach. No other restriction on the SRN is required. We apply our technique to the analysis of a flexible manufacturing system.
Adjoint Recovery of Superconvergent Functionals from Approximate Solutions of Partial Differential Equations
, 1998
"... Abstract. Motivated by applications in computational fluid dynamics, a method is presented for obtaining estimates of integral functionals, such as lift or drag, that have twice the order of accuracy of the computed flow solution on which they are based. This is achieved through error analysis that ..."
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Cited by 55 (9 self)
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Abstract. Motivated by applications in computational fluid dynamics, a method is presented for obtaining estimates of integral functionals, such as lift or drag, that have twice the order of accuracy of the computed flow solution on which they are based. This is achieved through error analysis that uses an adjoint PDE to relate the local errors in approximating the flow solution to the corresponding global errors in the functional of interest. Numerical evaluation of the local residual error together with an approximate solution to the adjoint equations may thus be combined to produce a correction for the computed functional value that yields the desired improvement in accuracy. Numerical results are presented for the Poisson equation in one and two dimensions and for the nonlinear quasionedimensional Euler equations. The theory is equally applicable to nonlinear equations in complex multidimensional domains and holds great promise for use in a range of engineering disciplines in which a few integral quantities are a key output of numerical approximations. Key words. PDEs, adjoint equations, error analysis, superconvergence AMS subject classifications. 65G99, 76N15 PII. S0036144598349423
Contact Sensing from Force Measurements
 International Journal of Robotics Research
, 1990
"... location of a contact, the force at the interface and the moment about the contact normals. Called "intrinsic" contact sensing for the use of in ternal force and torque measurements, this method allows for practical devices which provide simple, relevant contact information in practical robotic ..."
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Cited by 43 (2 self)
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location of a contact, the force at the interface and the moment about the contact normals. Called "intrinsic" contact sensing for the use of in ternal force and torque measurements, this method allows for practical devices which provide simple, relevant contact information in practical robotic applications. Such sensors have been used in conjunction with robot hands to identify objects, determine surface friction, detect slip, augment grasp stability, measure object mass, probe surfaces, control collision and a variety of other useful tasks. This paper describes the theoretical basis for their operation and provides a framework for future device design.
Is Gauss Quadrature Better Than Clenshaw–Curtis?
, 2008
"... We compare the convergence behavior of Gauss quadrature with that of its younger brother, Clenshaw–Curtis. Sevenline MATLAB codes are presented that implement both methods, and experiments show that the supposed factorof2 advantage of Gauss quadrature is rarely realized. Theorems are given to exp ..."
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Cited by 40 (3 self)
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We compare the convergence behavior of Gauss quadrature with that of its younger brother, Clenshaw–Curtis. Sevenline MATLAB codes are presented that implement both methods, and experiments show that the supposed factorof2 advantage of Gauss quadrature is rarely realized. Theorems are given to explain this effect. First, following O’Hara and Smith in the 1960s, the phenomenon is explained as a consequence of aliasing of coefficients in Chebyshev expansions. Then another explanation is offered based on the interpretation of a quadrature formula as a rational approximation of log((z +1)/(z − 1)) in the complex plane. Gauss quadrature corresponds to Padé approximation at z = ∞. Clenshaw–Curtis quadrature corresponds to an approximation whose order of accuracy at z = ∞ is only half as high, but which is nevertheless equally accurate near [−1, 1].
Stability of Block Algorithms with Fast Level 3 BLAS
 ACM Trans. Math. Soft
, 1992
"... . Block algorithms are becoming increasingly popular in matrix computations. Since their basic unit of data is a submatrix rather than a scalar they have a higher level of granularity than point algorithms, and this makes them wellsuited to highperformance computers. The numerical stability of the ..."
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Cited by 37 (15 self)
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. Block algorithms are becoming increasingly popular in matrix computations. Since their basic unit of data is a submatrix rather than a scalar they have a higher level of granularity than point algorithms, and this makes them wellsuited to highperformance computers. The numerical stability of the block algorithms in the new linear algebra program library LAPACK is investigated here. It is shown that these algorithms have backward error analyses in which the backward error bounds are commensurate with the error bounds for the underlying level 3 BLAS (BLAS3). One implication is that the block algorithms are as stable as the corresponding point algorithms when conventional BLAS3 are used. A second implication is that the use of BLAS3 based on fast matrix multiplication techniques affects the stability only insofar as it increases the constant terms in the normwise backward error bounds. For linear equation solvers employing LU factorization it is shown that fixed precision iterative re...
Bandwidthconstrained distributed estimation for wireless sensor networks  Part I: Gaussian Case
 IEEE TRANS. SIGNAL PROCESS
, 2006
"... We study deterministic meanlocation parameter estimation when only quantized versions of the original observations are available, due to bandwidth constraints. When the dynamic range of the parameter is small or comparable with the noise variance, we introduce a class of maximumlikelihood estimat ..."
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Cited by 34 (3 self)
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We study deterministic meanlocation parameter estimation when only quantized versions of the original observations are available, due to bandwidth constraints. When the dynamic range of the parameter is small or comparable with the noise variance, we introduce a class of maximumlikelihood estimators that require transmitting just one bit per sensor to achieve an estimation variance close to that of the (clairvoyant) sample mean estimator. When the dynamic range is comparable or larger than the noise standard deviation, we show that an optimum quantization step exists to achieve the best possible variance for a given bandwidth constraint. We will also establish that in certain cases the sample mean estimator formed by quantized observations is preferable for complexity reasons. We finally touch upon algorithm implementation issues and guarantee that all the numerical maximizations required by the proposed estimators are concave.
A comparison of Gaussian and mean curvatures estimation methods on triangular meshes
 In: ICRA
, 2003
"... Estimating intrinsic geometric properties of a surface from a polygonal mesh obtained from range data is an important stage of numerous algorithms in computer and robot vision, computer graphics, geometric modeling, industrial and biomedical engineering. This work considers different computational s ..."
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Cited by 30 (0 self)
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Estimating intrinsic geometric properties of a surface from a polygonal mesh obtained from range data is an important stage of numerous algorithms in computer and robot vision, computer graphics, geometric modeling, industrial and biomedical engineering. This work considers different computational schemes for local estimation of intrinsic curvature geometric properties. Five different algorithms and their modifications were tested on triangular meshes that represent tesselations of synthetic geometric models. The results were compared with the analytically computed values of the Gaussian and mean curvatures of the non uniform rational Bspline (NURBs) surfaces, these meshes originated from. This work manifests the best algorithms suited for total (Gaussian) and mean curvature estimation, and shows that indeed different alogrithms should be employed to compute the Gaussian and mean curvatures.
Advances in DerivativeFree State Estimation for Nonlinear Systems
, 2000
"... In this paper we show that it has considerable advantages to use polynomial approximations obtained with an interpolation formula for derivation of state estimators for nonlinear systems. The estimators become more accurate than estimators based on Taylor approximations; yet the implementation is si ..."
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Cited by 26 (0 self)
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In this paper we show that it has considerable advantages to use polynomial approximations obtained with an interpolation formula for derivation of state estimators for nonlinear systems. The estimators become more accurate than estimators based on Taylor approximations; yet the implementation is significantly simpler as no derivatives are required. Thus, it is believed that estimators derived in this way can replace wellknown filters, such as the extended Kalman filter (EKF) and its higher order relatives, in most practical applications. In addition to proposing a new set of state estimators, the paper also unifies recent developments in derivativefree state estimation.
On the Adaptive Numerical Solution of Nonlinear Partial Differential Equations in Wavelet Bases
, 1996
"... This work develops fast and adaptive algorithms for numerically solving nonlinear partial differential equations of the form u t = Lu +N f(u) where L and N are linear differential operators and f(u) is a nonlinear function. These equations are adaptively solved by projecting the solution u and the o ..."
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Cited by 25 (3 self)
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This work develops fast and adaptive algorithms for numerically solving nonlinear partial differential equations of the form u t = Lu +N f(u) where L and N are linear differential operators and f(u) is a nonlinear function. These equations are adaptively solved by projecting the solution u and the operators L and N into a wavelet basis. Vanishing moments of the basis functions permit a sparse representation of the solution and operators. Using these sparse representations fast and adaptive algorithms that apply operators to functions and evaluate nonlinear functions, are developed for solving evolution equations. For a wavelet representation of the solution u that contains N s significant coefficients, the algorithms update the solution using O(N s ) operations. The approach is applied to a number of examples and numerical results are given. 1 Introduction This paper is concerned with the fast, adaptive numerical solution of nonlinear partial differential equations having solutions...