Continuous and discrete least-squares approximation by radial basis functions on spheres
Journal of Approximation Theory, 2006 Let \(S^n\) be the \(n\)-dimensional sphere in \(\mathbb R^n\) and \(A=\{U_j,\psi_j\}_{j=1}^m\) be an atlas for \(S^n\), i.e. open sets \(U_j\subset S^n\) cover \(S^n\), \(\psi_j\) are homeomorphic from \(U_j\) to the unit ball \(B(0,1)\subset \mathbb R^n\) and \(\psi_i\circ \psi_j^{-1}\) are \(C^{\infty}\) on \(\psi_j(U_j\cap U_i)\). Let \(\{\chi_j\}_{
Le Gia, Q. T. +3 more
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Stable and Accurate Least Squares Radial Basis Function Approximations on Bounded Domains
SIAM Journal on Numerical AnalysisThe computation of global radial basis function (RBF) approximations requires the solution of a linear system which, depending on the choice of RBF parameters, may be ill-conditioned. We study the stability and accuracy of approximation methods using the Gaussian RBF in all scaling regimes of the associated shape parameter.
Ben Adcock, Daan Huybrechs, Cecile Piret
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Numerical Implementation of Meshless Methods for Beam Problems
Archives of Civil Engineering, 2012 For solving a partial different equation by a numerical method, a possible alternative may be either to use a mesh method or a meshless method. A flexible computational procedure for solving 1D linear elastic beam problems is presented that currently ...
Rosca V. E., Leitāo V. M. A.
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Quantile Regression under Misspecification, with an Application to the U.S. Wage Structure [PDF]
Quantile regression(QR) fits a linear model for conditional quantiles, just as ordinary least squares (OLS) fits a linear model for conditional means. An attractive feature of OLS is that it gives the minimum mean square error linear approximation to the
Ivan Fernandez-Val +2 more
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The approximation function of bridge deck vibration derived from the measured eigenmodes
International Journal of Applied Mathematics and Computer Science, 2017 This article deals with a method of how to acquire approximate displacement vibration functions. Input values are discrete, experimentally obtained mode shapes.
Sokol Milan +3 more
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Fast multi-dimensional scattered data approximation with Neumann boundary conditions
, 2003 An important problem in applications is the approximation of a function $f$ from a finite set of randomly scattered data $f(x_j)$. A common and powerful approach is to construct a trigonometric least squares approximation based on the set of exponentials
Grishin, Denis, Strohmer, Thomas
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Efficient least squares approximation and collocation methods using radial basis functions
Journal of Computational and Applied Mathematics23 pages, 10 ...
Zhou, Yiqing, Huybrechs, Daan
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On Convex Quadratic Approximation [PDF]
In this paper we prove the counterintuitive result that the quadratic least squares approximation of a multivariate convex function in a finite set of points is not necessarily convex, even though it is convex for a univariate convex function.
Hertog, D. den, Klerk, E. de, Roos, J.
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Semiparametric Estimation of Instrumental Variable Models for Causal Effects [PDF]
This article introduces a new class of instrumental variable (IV) estimators of causal treatment effects for linear and nonlinear models with covariates.
Alberto Abadie
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Deep reinforcement learning using least‐squares truncated temporal‐difference
CAAI Transactions on Intelligence TechnologyPolicy evaluation (PE) is a critical sub‐problem in reinforcement learning, which estimates the value function for a given policy and can be used for policy improvement.
Junkai Ren +5 more
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