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Local integration of population dynamics via moving least squares approximation
Engineering with Computers, 2016This paper applies an approach based on the Galerkin and collocation methods so-called meshless local Petrov---Galerkin (MLPG) method to treat a nonlinear partial integro-differential equation arising in population dynamics. In the proposed method, the MLPG method is applied to the interior nodes while the meshless collocation method is used for the ...
E. Shivanian
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Moving Least Squares Approximation
Interdisciplinary Mathematical Sciences, 2007exaly +2 more sources
Moving least-squares approximations for linearly-solvable MDP
2011 IEEE Symposium on Adaptive Dynamic Programming and Reinforcement Learning (ADPRL), 2011By introducing Linearly-solvable Markov Decision Process (LMDP), a general class of nonlinear stochastic optimal control problems can be reduced to solving linear problems. However, in practice, LMDP defined on continuous state space remain difficult due to high dimensionality of the state space.
Mingyuan Zhong 0002, Emanuel Todorov
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Approximating surfaces by moving total least squares method
Applied Mathematics and Computation, 1998We suggest a method for generating a surface approximating the given data $(x_i,y_i,z_i)inR^3$, $i=1,ldots,m$,assuming that the errors can occur both in the independent variables $x$ and $y$, as well as in the dependent variable $z$. Our approach is based on the moving total least squares method,where the local approximants (local planes) are ...
Scitovski, Rudolf +2 more
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Error estimates for moving least square approximations
Applied Numerical Mathematics, 2001We obtain error estimates for moving least square approximations in the one-dimensional case. For the application of this method to the numerical solution of differential equations it is fundamental to have error estimates for the approximations of derivatives.
Armentano, María G., Durán, Ricardo G.
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Fast least-squares polynomial approximation in moving time windows
1997 IEEE International Conference on Acoustics, Speech, and Signal Processing, 2002Only a few time series methods are applicable to signal trend analysis under real-time conditions. The use of orthogonal polynomials for least-squares approximations on discrete data turned out to be very efficient for providing estimators in the time domain.
Erich Fuchs, Klaus Donner
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Adaptive Moving Least Square Approximations and Its Application
AIP Conference Proceedings, 2010In Moving Least Square approximation, the nodal connectivity varies from point to point depending upon the domain of influence. Widely accepted rules about how to choose radius of influence do not exist. Since radius of influence will greatly effect the numerical accuracy, especially for high gradient and fast oscillatory problem.
Yuan Zhanbin +6 more
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Direct approximation on spheres using generalized moving least squares
BIT Numerical Mathematics, 2017This paper presents a moving square method on the sphere of \(\mathbb R^d\) that differs from the classical one considering a different approach -- the so-called direct approach. Let \(X\) be the set of points in the sphere. The classical method is based on the approximation of a certain function \(u\) by a set of functions and requires the action of ...
D. Mirzaei
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Error Estimates in Sobolev Spaces for Moving Least Square Approximations
SIAM Journal on Numerical Analysis, 2001Let \(\Omega\) be a convex set in \(\mathbb{R}^N\) and let \(\xi_{1}, \xi_{2},\dots,\xi_{n}\) be given points in \(\Omega\). Furthermore let \(\Phi_{R}\) be a function with values in \([0,1]\) and support in the ball \(\{ z|\|z\|\leq R \}\). Denote by \(\mathcal{P}_{m}\) the set of polynomials of degree \(m\) or less and \(s\) its dimension. Let \(p_{1}
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