Results 1  10
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347
Quadraturebased methods for obtaining approximate solutions to nonlinear asset pricing models
 ECONOMETRICA
, 1991
"... ..."
Discrepancy as a Quality Measure for Sample Distributions
, 1991
"... Discrepancy, a scalar measure of sample point equidistribution, is discussed in the context of Computer Graphics sampling problems. Several sampling strategies and their discrepancy characteristics are examined. The relationship between image error and the discrepancy of the sampling patterns used t ..."
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Cited by 79 (7 self)
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Discrepancy, a scalar measure of sample point equidistribution, is discussed in the context of Computer Graphics sampling problems. Several sampling strategies and their discrepancy characteristics are examined. The relationship between image error and the discrepancy of the sampling patterns used to generate the imaqge is established. The definition of discrepancy is extended to nonuniform sampling patterns.
Physically Based Lighting Calculations for Computer Graphics
, 1991
"... Realistic image generation is presented in a theoretical formulation that builds from previous work on the rendering equation. Previous and new solution techniques for the global illumination are discussed in the context of this formulation. The basic ..."
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Cited by 78 (13 self)
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Realistic image generation is presented in a theoretical formulation that builds from previous work on the rendering equation. Previous and new solution techniques for the global illumination are discussed in the context of this formulation. The basic
The Natural Element Method In Solid Mechanics
, 1998
"... The application of the Natural Element Method (NEM) (Traversoni, 1994; Braun and Sambridge, 1995) to boundary value problems in twodimensional small displacement elastostatics is presented. The discrete model of the domain \Omega consists of a set of distinct nodes N , and a polygonal descripti ..."
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Cited by 61 (14 self)
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The application of the Natural Element Method (NEM) (Traversoni, 1994; Braun and Sambridge, 1995) to boundary value problems in twodimensional small displacement elastostatics is presented. The discrete model of the domain \Omega consists of a set of distinct nodes N , and a polygonal description of the boundary @ In the Natural Element Method, the trial and test functions are constructed using natural neighbor interpolants. These interpolants are based on the Voronoi tessellation of the set of nodes N . The interpolants are smooth (C NEM is identical to linear finite elements. The NEM interpolant is strictly linear between adjacent nodes on the boundary of the convex hull, which facilitates imposition of essential boundary conditions. A methodology to model material discontinuities and nonconvex bodies (cracks) using NEM is also described.
Arbitrary high order discontinuous Galerkin schemes
 GOUDON & E. SONNENDRUCKER EDS). IRMA SERIES IN MATHEMATICS AND THEORETICAL PHYSICS
, 2005
"... In this paper we apply the ADER one step time discretization to the Discontinuous Galerkin framework for hyperbolic conservation laws. In the case of linear hyperbolic systems we obtain a quadraturefree explicit singlestep scheme of arbitrary order of accuracy in space and time on Cartesian and tr ..."
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Cited by 50 (7 self)
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In this paper we apply the ADER one step time discretization to the Discontinuous Galerkin framework for hyperbolic conservation laws. In the case of linear hyperbolic systems we obtain a quadraturefree explicit singlestep scheme of arbitrary order of accuracy in space and time on Cartesian and triangular meshes. The ADERDG scheme does not need more memory than a first order explicit Euler timestepping scheme. This becomes possible because of an extensive use of the governing equations inside the numerical scheme. In the nonlinear case, quadrature of the ADERDG scheme in space and time is performed with Gaussian quadrature formulae of suitable order of accuracy. We show numerical convergence results for the linearized Euler equations up to 10th order of accuracy in space and time on Cartesian and triangular meshes. Numerical results for the nonlinear Euler equations up to 6th order of accuracy in space and time are provided as well. In this paper we also show the possibility of applying a linear reconstruction operator of the order 3N + 2 to the degrees of freedom of the DG method resulting in a numerical scheme of the order 3N + 3 on Cartesian grids where N is the order of the original basis functions before reconstruction.
Methods for Approximating Integrals in Statistics with Special Emphasis on Bayesian Integration Problems
 Statistical Science
"... This paper is a survey of the major techniques and approaches available for the numerical approximation of integrals in statistics. We classify these into five broad categories; namely, asymptotic methods, importance sampling, adaptive importance sampling, multiple quadrature and Markov chain method ..."
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Cited by 49 (5 self)
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This paper is a survey of the major techniques and approaches available for the numerical approximation of integrals in statistics. We classify these into five broad categories; namely, asymptotic methods, importance sampling, adaptive importance sampling, multiple quadrature and Markov chain methods. Each method is discussed giving an outline of the basic supporting theory and particular features of the technique. Conclusions are drawn concerning the relative merits of the methods based on the discussion and their application to three examples. The following broad recommendations are made. Asymptotic methods should only be considered in contexts where the integrand has a dominant peak with approximate ellipsoidal symmetry. Importance sampling, and preferably adaptive importance sampling, based on a multivariate Student should be used instead of asymptotics methods in such a context. Multiple quadrature, and in particular subregion adaptive integration, are the algorithms of choice for...
The Multilevel Finite Element Method for Adaptive Mesh Optimization and Visualization of Volume Data
 In Proceedings Visualization
, 1997
"... Multilevel representations and mesh reduction techniques have been used for accelerating the processing and the rendering of large datasets representing scalar or vector valued functions defined on complex 2 or 3 dimensional meshes. We present a method based on finite element approximations which co ..."
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Cited by 45 (5 self)
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Multilevel representations and mesh reduction techniques have been used for accelerating the processing and the rendering of large datasets representing scalar or vector valued functions defined on complex 2 or 3 dimensional meshes. We present a method based on finite element approximations which combines these two approaches in a new and unique way that is conceptually simple and theoretically sound. The main idea is to consider mesh reduction as an approximation problem in appropriate finite element spaces. Starting with a very coarse triangulation of the functional domain a hierarchy of highly nonuniform tetrahedral (or triangular in 2D) meshes is generated adaptively by local refinement. This process is driven by controlling the local error of the piecewise linear finite element approximation of the function on each mesh element. A reliable and efficient computation of the global approximation error combined with a multilevel preconditioned conjugate gradient solver are the key co...
Weak approximation of stochastic differential equations and application to derivative pricing
, 2006
"... The authors present a new simple algorithm to approximate weakly stochastic differential equations in the spirit of [10][16]. They apply it to the problem of pricing Asian options under the Heston stochastic volatility model, and compare it with other known methods. It is shown that the combination ..."
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Cited by 44 (1 self)
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The authors present a new simple algorithm to approximate weakly stochastic differential equations in the spirit of [10][16]. They apply it to the problem of pricing Asian options under the Heston stochastic volatility model, and compare it with other known methods. It is shown that the combination of the suggested algorithm and quasiMonte Carlo methods makes computations extremely fast.
McLaren’s improved snub cube and other new spherical designs in three dimensions
 Discrete and Computational Geometry
, 1996
"... Evidence is presented to suggest that, in three dimensions, spherical 6designs with N ..."
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Cited by 40 (1 self)
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Evidence is presented to suggest that, in three dimensions, spherical 6designs with N
Exposure in Wireless Sensor Networks: Theory and Practical Solutions
 Wireless Networks
, 2002
"... Wireless adhoc sensor networks have the potential to provide the missing interface between the physical world and the Internet, thus impacting a large number of users. This connection will enable computational treatments of the physical world in ways never before possible. In this far reaching scen ..."
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Cited by 40 (4 self)
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Wireless adhoc sensor networks have the potential to provide the missing interface between the physical world and the Internet, thus impacting a large number of users. This connection will enable computational treatments of the physical world in ways never before possible. In this far reaching scenario, quality of service can be expressed in terms of accuracy and/or latency of observing events and overall state of the physical world. Consequently, one of the fundamental problems in sensor networks is the calculation of coverage, which can be defined as a measure of the ability to detect objects within a sensor filed. Exposure is directly related to coverage in that it is an integral measure of how well the sensor network can observe an object, moving on an arbitrary path, over a period of time.