MATHICSE Technical Report : Discrete least squares polynomial approximation with random evaluations – application to parametric and stochastic elliptic PDES
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We study the least-squares regression problem over a Hilbert space, covering nonparametric regression over a reproducing kernel Hilbert space as a special case. We rst investigate regularized algorithms adapted to a projection operator on a closed subspace ...
Advances in high-speed imaging techniques have opened new possibilities for capturing ultrafast phenomena such as light propagation in air or through media. Capturing light in flight in three-dimensional xyt space has been reported based on various types o ...
Quasi-Newton (qN) techniques approximate the Newton step by estimating the Hessian using the so-called secant equations. Some of these methods compute the Hessian using several secant equations but produce non-symmetric updates. Other quasi-Newton schemes, ...
The present work deals with rational model order reduction methods based on the single-point Least-Square (LS) Padé approximation techniques introduced in Bonizzoni et al. (ESAIM Math. Model. Numer. Anal., 52(4), 1261–1284 2018, Math. Comput. 89, 1229–1257 ...
Dynamic Networks have been introduced in the literature to solve multi-sensor fusion problems for navigation and mapping. They have been shown to outperform conventional methods in challenging scenarios, such as corridor mapping or self-calibration. In thi ...
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 present a technique for the approximation of a class of Hilbert space--valued maps which arise within the framework of model order reduction (MOR) for parametric partial differential equations, whose solution map has a meromorphic structure. Our MOR str ...
Without resorting to complex numbers or any advanced topological arguments, we show that any real polynomial of degree greater than two always has a real quadratic polynomial factor, which is equivalent to the fundamental theorem of algebra. The proof uses ...
Visual crowding is the inability to perceive elements within clutter. Traditional crowding models, such as pooling, predict that performance deteriorates when flankers are added. However, this prediction has been disproved. For example, performance was fou ...
We investigate regularized algorithms combining with projection for least-squares regression problem over a Hilbert space, covering nonparametric regression over a reproducing kernel Hilbert space. We prove convergence results with respect to variants of n ...