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The use of T-splines enhance our spline methods with local refinement capability and numerical tests show the efficiency and the accuracy of the techniques we propose.

The choice of discontinuous trial functions not only has the advantage of easing local refinement, it also facilitates the use of efficient sweep-based solvers due to decoupling of unknowns on a large scale thereby approaching the efficiency of discrete ordinates methods with local angular resolution.

In [ 2] a combination of global stochastic methods with local methods has been proposed.

In order to surmount this difficulty, hybrid methods and metaheuristics that have been recently developed which combine global stochastic methods with local gradient based methods in two phases [ 47] or in several phases as in the scatter search based method eSS [ 23, 48].

Since the log likelihood is concave, the global optimum can be found using gradient methods, with local derivatives ∂ L ∂ α i (s ) = 〈 r i 〉 P D a t a (r | s ) − 〈 r i 〉 P (2 ) (r | s ), where < f(r)> P represents the expected value of some function of the response, f, with respect to the probability distribution P. Data were split into train and test sets.

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In this work, we integrate multivariate adaptive regression splines (MARS) method with local reweighting methods.

We present a nonoverlapping domain decomposition method with local Fourier basis applied to a model problem in liquid flames.

Modifying the Nyström method with local corrections for singular integrands allows the method to be applied to the inherently singular kernels of frequency-domain electromagnetic integral equations.

The LBGK method with local grid refinement has been shown to be an efficient and accurate tool for the simulation of incompressible, viscous flows over complex geometries.

Although the new problem is still nonlinear on the boundary, this problem no longer has the inequality constraint and can be solved by the semismooth Newton method with local superlinear convergence rate [7, 14].

Using LDA method with local generalised gradient corrections, the subject of the calculation included the adsorption of single-carbon species and double-carbon species on an activated diamond surface.

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