MATHICSE Technical Report : Analysis of the discrete $L^2$ projection on polynomial spaces with random evaluations
Graph Chatbot
Chat with Graph Search
Ask any question about EPFL courses, lectures, exercises, research, news, etc. or try the example questions below.
DISCLAIMER: The Graph Chatbot is not programmed to provide explicit or categorical answers to your questions. Rather, it transforms your questions into API requests that are distributed across the various IT services officially administered by EPFL. Its purpose is solely to collect and recommend relevant references to content that you can explore to help you answer your questions.
Weighted least squares polynomial approximation uses random samples to determine projections of functions onto spaces of polynomials. It has been shown that, using an optimal distribution of sample locations, the number of samples required to achieve quasi ...
We propose and analyse randomized cubature formulae for the numerical integration of functions with respect to a given probability measure μ defined on a domain Γ⊆ℝ^d, in any dimension d. Each cubature formula is conceived to be exact on a given finite dim ...
We present a technique for the approximation of a class of Hilbert space-valued maps which arise within the framework of Model Order Reduction for parametric partial differential equations, whose solution map has a meromorphic structure. Our MOR stategy co ...
We analyze the accuracy of the discrete least-squares approximation of a function u in multivariate polynomial spaces PΛ:=span{y↦yν:ν∈Λ} with Λ⊂N0d over the domain Γ:=[−1,1]d, based on the s ...
We consider the problem of sampling at unknown locations. We prove that, in this setting, if we take arbitrarily many samples of a polynomial or real bandlimited signal, it is possible to find another function in the same class, arbitrarily far away from t ...
The interface control domain decomposition (ICDD) method of Discacciati, Gervasio, and Quarteroni [SIAM J. Control Optim., 51 (2013), pp. 3434-3458, doi:10.1137/120890764; J. Coupled Syst. Multiscale Dyn., 1 (2013), pp. 372-392, doi:10.1166/jcsmd.2013.1026 ...
This work considers the infinite-time discounted optimal control problem for continuous time input-affine polynomial dynamical systems subject to polynomial state and box input constraints. We propose a sequence of sum-of-squares (SOS) approximations of th ...
Optimization is a fundamental tool in modern science. Numerous important tasks in biology, economy, physics and computer science can be cast as optimization problems. Consider the example of machine learning: recent advances have shown that even the most s ...
We present a sampling theory for a class of binary images with finite rate of innovation (FRI). Every image in our model is the restriction of \mathds1{p≤0} to the image plane, where \mathds1 denotes the indicator function and p is some r ...
Weighted least squares polynomial approximation uses random samples to determine projections of functions onto spaces of polynomials. It has been shown that, using an optimal distribution of sample locations, the number of samples required to achieve quasi ...
