On low-rank approximability of solutions to high-dimensional operator equations and eigenvalue problems
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We consider a critical point u(0) of a functional f is an element of C-1 (H, R), where H is a real Hilbert space, and formulate criteria ensuring that u(0) lies in a potential well of f without supposing that f' is Frechet differentiable at u(0). The deriv ...
Pergamon-Elsevier Science Ltd2017
We analyse the existence of multiple critical points for an even functional J : H -> R in the following context: the Hilbert space H can be split into an orthogonal sum H = Y circle plus Z in such a way that inf{J(u) : u is an element of Z and parallel to ...
Springer Heidelberg2016
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Next-generation radio-interferometers face a computing challenge with respect to the imaging techniques that can be applied in the big data setting in which they are designed. Dimensionality reduction can thus provide essential savings of computing resourc ...
2017
This paper deals with asymptotic bifurcation, first in the abstract setting of an equation G(u) = lambda u, where G acts between real Hilbert spaces and lambda is an element of R, and then for square-integrable solutions of a second order non-linear ellipt ...
Elsevier Science Bv2015
In this thesis, we present a Riemannian framework for the solution of high-dimensional optimization problems with an underlying low-rank tensor structure. Here, the high-dimensionality refers to the size of the search space, while the cost function is scal ...
EPFL2016
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Mining useful clusters from high dimensional data has received significant attention of the computer vision and pattern recognition community in the recent years. Linear and non-linear dimensionality reduction has played an important role to overcome the c ...
The focus of this thesis is on developing efficient algorithms for two important problems arising in model reduction, estimation of the smallest eigenvalue for a parameter-dependent Hermitian matrix and solving large-scale linear matrix equations, by extra ...
EPFL2016
The paper introduces a functional time series (lagged) regression model. The impulse-response coefficients in such a model are operators acting on a separable Hilbert space, which is the function space L-2 in applications. A spectral approach to the estima ...
Wiley-Blackwell2015
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We consider the numerical approximation of high order Partial Differential Equations (PDEs) defined on surfaces in the three dimensional space, with particular emphasis on closed surfaces. We consider computational domains that can be represented by B-spli ...
MATHICSE2015
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We consider the numerical approximation of high order Partial Differential Equations (PDEs) defined on surfaces in the three dimensional space, with particular emphasis on closed surfaces. We consider computational domains that can be represented by B-spli ...
