Results 21 to 30 of about 949,851 (307)
Quasi-interpolation in Spline Spaces: Local Stability and Approximation Properties
Trends in Computational and Applied Mathematics, 2023 In this work we analyze the approximation error in Sobolev norms for quasi-interpolation operators in spline spaces. We establish in a general way the hypotheses on a quasi-interpolant to achieve the optimal order of approximation.
M. E. Castillo, E. M. Garau
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Numerical Homogenization of Heterogeneous Fractional Laplacians [PDF]
, 2017 In this paper, we develop a numerical multiscale method to solve the fractional Laplacian with a heterogeneous diffusion coefficient. When the coefficient is heterogeneous, this adds to the computational costs.
Brown, Donald L. +2 more
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C1-Cubic Quasi-Interpolation Splines over a CT Refinement of a Type-1 Triangulation
Mathematics, 2022 C1 continuous quasi-interpolating splines are constructed over Clough–Tocher refinement of a type-1 triangulation. Their Bernstein–Bézier coefficients are directly defined from the known values of the function to be approximated, so that a set of ...
Haithem Benharzallah +2 more
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Quasi-interpolation by means of filter-banks [PDF]
, 2010 We consider the problem of approximating a regular function f(t) from its samples, f(nT), taken in a uniform grid. Quasi-interpolation schemes approximate f(t) with a dilated version of a linear combination of shifted versions of a kernel ??(t ...
Perez Villalon, Gerardo
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Multiscale Partition of Unity [PDF]
, 2013 We introduce a new Partition of Unity Method for the numerical homogenization of elliptic partial differential equations with arbitrarily rough coefficients. We do not restrict to a particular ansatz space or the existence of a finite element mesh.
C.A. Duarte +11 more
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Approximate Hermite quasi-interpolation [PDF]
Applicable Analysis, 2008 In this paper we derive approximate quasi-interpolants when the values of a function $u$ and of some of its derivatives are prescribed at the points of a uniform grid. As a byproduct of these formulas we obtain very simple approximants which provide high order approximations for solutions to elliptic differential equations with constant coefficients.
LANZARA, Flavia, V. Maz'Ya, G. Schmidt
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Mathematical Problems in Engineering, 2021 In this paper, a Crank–Nicolson finite difference scheme based on cubic B-spline quasi-interpolation has been derived for the solution of the coupled Burgers equations with the Caputo–Fabrizio derivative.
M. Taghipour, H. Aminikhah
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Quasi‐interpolation by splines on the uniform knot sets
Mathematical Modelling and Analysis, 2007 In the case of uniform grids, the error of the spline interpolant of a function defined on R has been well estimated. On the basis of the spline interpolation formula for functions defined on R we derive quasi‐interpolation formulae for functions defined
Evely Leetma
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QuITO: Numerical software for constrained nonlinear optimal control problems
SoftwareX, 2023 We introduce the MATLAB-based software QuITO (Quasi-Interpolation based Trajectory Optimization) to numerically solve a wide class of constrained nonlinear optimal control problems (OCP). The solver is based on the QuITO (the same abbreviation) algorithm,
Siddhartha Ganguly +4 more
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A Neural Network Approximation Based on a Parametric Sigmoidal Function
Mathematics, 2019 It is well known that feed-forward neural networks can be used for approximation to functions based on an appropriate activation function. In this paper, employing a new sigmoidal function with a parameter for an activation function, we consider a ...
Beong In Yun
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