Algorithmes numériques et calcul haute performance - Chaire CADMOS

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Publications associées (333)

Fundamental Group And Pluridifferentials On Compact Kahler Manifolds

Yohan Cédric Loup Brunebarbe

A compact Kahler manifold X is shown to be simply connected if its 'symmetric cotangent algebra' is trivial. Conjecturally, such a manifold should even be rationally connected. The relative version is also shown: a proper surjective connected holomorphic m ...

Independent Univ Moscow-Ium2016

MATHICSE Technical Report : Preconditioned low-rank Riemannian optimization for linear systems with tensor product structure

Daniel Kressner, Michael Maximilian Steinlechner

The numerical solution of partial differential equations on high-dimensional domains gives rise to computationally challenging linear systems. When using standard discretization techniques, the size of the linear system grows exponentially with the number ...

MATHICSE2015

MATHICSE Technical Report : Multi-index stochastic collocation convergence rates for random PDEs with parametric regularity

Fabio Nobile, Lorenzo Tamellini

We analyze the recent Multi-index Stochastic Collocation (MISC) method for computing statistics of the solution of a partial differential equation with random data, where the random coefficient is parametrized by means of a countable sequence of terms in a ...

MATHICSE2015

This work is concerned with the numerical solution of large-scale linear matrix equations A1XB1T++AKXBKT=C. The most straightforward approach computes XRmxn from the solution of an mn x mn linear system, typically limiting the feasible values of m,n to a f ...

Wiley-Blackwell2015

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Gaussian random fields are widely used as building blocks for modeling stochastic processes. This paper is concerned with the efficient representation of d-point correlations for such fields, which in turn enables the representation of more general stochas ...

2015

MATHICSE Technical Report : Accelerated filtering on graphs using Lanczos method

Pierre Vandergheynst, Daniel Kressner, Nathanaël Perraudin, Ana Susnjara

Sinal-processing on graphs has developed into a very active field of research during the last decade. In particular, the number of applications using frames con-structed from graphs, like wavelets on graphs, has substantially increased. To attain scalabili ...

MATHICSE2015

MATHICSE Technical Report: Reduced basis methods: from low-rank matrices to low-rank tensor

Daniel Kressner, Jonas Ballani

We propose a novel combination of the reduced basis method with low-rank tensor techniques for the efficient solution of parameter-dependent linear systems in the case of several parameters. This combination, called rb Tensor, consists of three ingredients ...

MATHICSE2015

This work is concerned with approximating the smallest eigenvalue of a parameter-dependent Hermitian matrix A(μ) for many parameter values μ ∈ RP. The design of reliable and efficient algorithms for addressing this task is of importance in a variety of app ...

MATHICSE2015

MATHICSE Technical Report : A theoretical study of COmpRessed SolvING for advection-diffusion-reaction problems

Fabio Nobile, Simone Brugiapaglia

We present a theoretical analysis of the CORSING (COmpRessed SolvING) method for the numerical approximation of partial differential equations based on compressed sensing. In particular, we show that the best s-term approximation of the weak solution of a ...

MATHICSE2015

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The parareal algorithm seeks to extract parallelism in the time-integration direction of time-dependent differential equations. While it has been applied with success to a wide range of problems, it suffers from some stability issues when applied to non-di ...

2015