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170
Barycentric Lagrange Interpolation
, 2004
"... Barycentric interpolation is a variant of Lagrange polynomial interpolation that is fast and stable. It deserves to be known as the standard method of polynomial interpolation. ..."
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Cited by 129 (6 self)
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Barycentric interpolation is a variant of Lagrange polynomial interpolation that is fast and stable. It deserves to be known as the standard method of polynomial interpolation.
Automatic, TemplateBased RunTime Specialization: Implementation and Experimental Study
 In International Conference on Computer Languages
, 1998
"... Specializing programs with respect to runtime values has been shown to drastically improve code performance on realistic programs ranging from operating systems to graphics. Recently, various approaches to specializing code at runtime have been proposed. However, these approaches still suffer from ..."
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Cited by 61 (12 self)
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Specializing programs with respect to runtime values has been shown to drastically improve code performance on realistic programs ranging from operating systems to graphics. Recently, various approaches to specializing code at runtime have been proposed. However, these approaches still suffer from shortcomings that limit their applicability: they are manual, too expensive, or require programs to be written in a dedicated language. We solve these problems by introducing new techniques to implement runtime specialization. The key to our approach is the use of code templates. Templates are automatically generated from ordinary programs and are optimized before run time, allowing highquality code to be quickly generated at run time. Experimental results obtained on scientific and graphics code indicate that our approach is highly effective. Little runtime overhead is introduced, since code generation primarily consists of copying instructions. Runtime specialized programs run up to 1...
Filter Pattern Search Algorithms for Mixed Variable Constrained Optimization Problems
 SIAM Journal on Optimization
, 2004
"... A new class of algorithms for solving nonlinearly constrained mixed variable optimization problems is presented. This class combines and extends the AudetDennis Generalized Pattern Search (GPS) algorithms for bound constrained mixed variable optimization, and their GPSfilter algorithms for gene ..."
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Cited by 55 (6 self)
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A new class of algorithms for solving nonlinearly constrained mixed variable optimization problems is presented. This class combines and extends the AudetDennis Generalized Pattern Search (GPS) algorithms for bound constrained mixed variable optimization, and their GPSfilter algorithms for general nonlinear constraints. In generalizing existing algorithms, new theoretical convergence results are presented that reduce seamlessly to existing results for more specific classes of problems. While no local continuity or smoothness assumptions are required to apply the algorithm, a hierarchy of theoretical convergence results based on the Clarke calculus is given, in which local smoothness dictate what can be proved about certain limit points generated by the algorithm. To demonstrate the usefulness of the algorithm, the algorithm is applied to the design of a loadbearing thermal insulation system. We believe this is the first algorithm with provable convergence results to directly target this class of problems.
Quaternions, interpolation and animation
, 1998
"... The main topics of this technical report are quaternions, their mathematical properties, and how they can be used to rotate objects. We introduce quaternion mathematics and discuss why quaternions are a better choice for implementing rotation than the wellknown matrix implementations. We then treat ..."
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Cited by 46 (0 self)
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The main topics of this technical report are quaternions, their mathematical properties, and how they can be used to rotate objects. We introduce quaternion mathematics and discuss why quaternions are a better choice for implementing rotation than the wellknown matrix implementations. We then treat different methods for interpolation between series of rotations. During this treatment we give complete proofs for the correctness of the important interpolation methods Slerp and Squad. Inspired by our treatment of the different interpolation methods we develop our own interpolation method called Spring based on a set of objective constraints for an optimal interpolation curve. This results in a set of differential equations, whose analytical solution meets these constraints. Unfortunately, the set of differential equations cannot be solved analytically. As an alternative we propose a numerical solution for the differential equations. The different interpolation methods are visualized and commented. Finally we provide a thorough comparison of the two most convincing methods (Spring and Squad). Thereby, this report provides a comprehensive
Artificial Neural Networks for Solving Ordinary and Partial Differential Equations,
 IEEE Transactions on Neural Networks, Volume 9, Issue
, 1998
"... AbstractWe present a method to solve initial and boundary value problems using artificial neural networks. A trial solution of the differential equation is written as a sum of two parts. The first part satisfies the initial/boundary conditions and contains no adjustable parameters. The second part ..."
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Cited by 32 (5 self)
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AbstractWe present a method to solve initial and boundary value problems using artificial neural networks. A trial solution of the differential equation is written as a sum of two parts. The first part satisfies the initial/boundary conditions and contains no adjustable parameters. The second part is constructed so as not to affect the initial/boundary conditions. This part involves a feedforward neural network containing adjustable parameters (the weights). Hence by construction the initial/boundary conditions are satisfied and the network is trained to satisfy the differential equation. The applicability of this approach ranges from single ordinary differential equations (ODE's), to systems of coupled ODE's and also to partial differential equations (PDE's). In this article, we illustrate the method by solving a variety of model problems and present comparisons with solutions obtained using the Galekrkin finite element method for several cases of partial differential equations. With the advent of neuroprocessors and digital signal processors the method becomes particularly interesting due to the expected essential gains in the execution speed. Index TermsCollocation method, finite elements, neural networks, neuroprocessors, ordinary differential equations, partial differential equations.
Transient Analysis of Markov Regenerative Stochastic Petri Nets: A Comparison of Approaches
 In 6th International Conference on Petri Nets and Performance Models  PNPM95
, 1995
"... In this paper we present and compare two different approaches for the transient solution of Markov regenerative stochastic Petri Nets: the method based on Markov regenerative theory and the method of supplementary variables. In both cases the equations that govern the marking process of the nonMark ..."
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Cited by 30 (12 self)
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In this paper we present and compare two different approaches for the transient solution of Markov regenerative stochastic Petri Nets: the method based on Markov regenerative theory and the method of supplementary variables. In both cases the equations that govern the marking process of the nonMarkovian stochastic Petri net are presented and then solved either in timedomain or using a LaplaceStieltjes transformation. We develop expressions for asymptotic computational costs and storage requirements. We also perform experimental studies to compare accuracy, time, and space complexity of the methods. 1 Introduction Stochastic Petri nets (SPNs) are well suited for the modelbased performance and dependability evaluation of complex systems. In the past few years, several papers were published dealing with the transient and stationary analysis of nonMarkovian SPNs in which, under certain structural restrictions, the firing times may be generally distributed. Besides the approach of ap...
Creating and rendering convolution surfaces,
 Computer Graphics Forum
, 1998
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The Effective Energy Transformation Scheme as a Special Continuation Approach to Global Optimization with Application to Molecular Conformation
 Preprint MCSP4420694, Argonne National Laboratory, Argonne
, 1996
"... This paper discusses a generalization of the function transformation scheme used in [4, 5, 19, 20] for global energy minimization applied to the molecular conformation problem. A mathematical theory for the method as a special continuation approach to global optimization is established. We show that ..."
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Cited by 24 (6 self)
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This paper discusses a generalization of the function transformation scheme used in [4, 5, 19, 20] for global energy minimization applied to the molecular conformation problem. A mathematical theory for the method as a special continuation approach to global optimization is established. We show that the method can transform a nonlinear objective function into a class of gradually deformed, but "smoother" or "easier" functions. An optimization procedure can then be applied to the new functions successively, to trace their solutions back to the original function. Two types of transformation are defined: isotropic and anisotropic. We show that both transformations can be applied to a large class of nonlinear partially separable functions including energy functions for molecular conformation. Methods to compute the transformation for these functions are given.
Scaling InternalState PolicyGradient Methods for POMDPs
 PROC. ICML02
, 2002
"... Policygradient methods have received increased attention recently as a mechanism for learning to act in partially observable environments. They have ..."
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Cited by 21 (0 self)
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Policygradient methods have received increased attention recently as a mechanism for learning to act in partially observable environments. They have