Related papers: Quasi-interpolation for high-dimensional function …
We present a method that allows efficient and safe approximation of model predictive controllers using kernel interpolation. Since the computational complexity of the approximating function scales linearly with the number of data points, we…
In this paper, a two-phase quasi-Newton scheme is proposed for solving an unconstrained optimization problem. The global convergence property of the scheme is provided under mild assumptions. The superlinear rate of the scheme is also…
We consider a framework for the construction of iterative schemes for operator equations that combine low-rank approximation in tensor formats and adaptive approximation in a basis. Under fairly general assumptions, we obtain a rigorous…
In this paper, we propose a fully discrete soft thresholding trigonometric polynomial approximation on $[-\pi,\pi],$ named Lasso trigonometric interpolation. This approximation is an $\ell_1$-regularized discrete least squares approximation…
To facilitate the numerical analysis of particle methods, we derive truncation error estimates for the approximate operators in a generalized particle method. Here, a generalized particle method is defined as a meshfree numerical method…
A number of basic image processing tasks, such as any geometric transformation require interpolation at subpixel image values. In this work we utilize the multidimensional coordinate Hermite spline interpolation defined on non-equal spaced,…
When using images to locate objects, there is the problem of correcting for distortion and misalignment in the images. An elegant way of solving this problem is to generate an error correcting function that maps points in an image to their…
Block-to-block interface interpolation operators are constructed for several common high-order finite difference discretizations. In contrast to conventional interpolation operators, these new interpolation operators maintain the strict…
In this article we design a novel quasi-regression Monte Carlo algorithm in order to approximate the solution of discrete time backward stochastic differential equations (BSDEs), and we analyze the convergence of the proposed method. The…
In simulation technology, computationally expensive objective functions are often replaced by cheap surrogates, which can be obtained by interpolation. Full grid interpolation methods suffer from the so-called curse of dimensionality,…
Quasi-Newton methods refer to a class of algorithms at the interface between first and second order methods. They aim to progress as substantially as second order methods per iteration, while maintaining the computational complexity of…
We introduce a discretization scheme for continuous localized frames using quasi-Monte Carlo integration and discrepancy theory. By generalizing classical concepts, we define a discrepancy measure on the entire phase space $\mathbb{R}^2$…
An interpolation error is an integral of the squared error of a regression model over a domain of interest. We consider the interpolation error for the case of misspecified Gaussian process regression: used covariance function differs from…
We consider a wide class of semi linear Hamiltonian partial differential equa- tions and their approximation by time splitting methods. We assume that the nonlinearity is polynomial, and that the numerical tra jectory remains at least uni-…
The statistical problem of parameter estimation in partially observed hypoelliptic diffusion processes is naturally occurring in many applications. However, due to the noise structure, where the noise components of the different coordinates…
This work presents a novel matrix-based method for constructing an approximation Hessian using only function evaluations. The method requires less computational power than interpolation-based methods and is easy to implement in matrix-based…
We revisit the classical kernel method of approximation/interpolation theory in a very specific context motivated by the desire to obtain a robust procedure to approximate discrete data sets by (super)level sets of functions that are merely…
We present novel model reduction methods for rapid solution of parametrized nonlinear partial differential equations (PDEs) in real-time or many-query contexts. Our approach combines reduced basis (RB) space for rapidly convergent…
Learning mappings of data on manifolds is an important topic in contemporary machine learning, with applications in astrophysics, geophysics, statistical physics, medical diagnosis, biochemistry, 3D object analysis. This paper studies the…
Video frame interpolation typically involves two steps: motion estimation and pixel synthesis. Such a two-step approach heavily depends on the quality of motion estimation. This paper presents a robust video frame interpolation method that…