On Iterative Solution of the Extended Normal Equations

Autor: Xavier Vasseur, Henri Calandra, Serge Gratton, Elisa Riccietti

Publikováno v: SIAM Journal on Matrix Analysis and Applications
SIAM Journal on Matrix Analysis and Applications, Society for Industrial and Applied Mathematics, 2020, 41 (4), pp.1571-1589. ⟨10.1137/19M1288644⟩

International audience; Given a full-rank matrix $A \in \mathbb{R}^{m\times n}$ ($m\geq n$), we consider a special class of linear systems $A^T\! Ax=A^T\! b+c$ with $x, c \in \mathbb{R}^{n}$ and $b \in \mathbb{R}^{m}$, which we refer to as the extend

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::e24ee64aec5beb22f4ebef5bb08b43ea
https://doi.org/10.1137/19m1288644

Numerical approximation of port-Hamiltonian systems for hyperbolic or parabolic PDEs with boundary control

Autor: Anass Serhani, Ghislain Haine, Xavier Vasseur, Andrea Brugnoli

Publikováno v: Journal of Applied Mathematics and Physics (JAMP)
Journal of Applied Mathematics and Physics (JAMP), Scientific Research Publishing, 2021, 09 (06), pp.1278-1321. ⟨10.4236/jamp.2021.96088⟩

We consider the design of structure-preserving discretization methods for the solution of systems of boundary controlled Partial Differential Equations (PDEs) thanks to the port-Hamiltonian formalism. We first provide a novel general structure of inf

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::0e48877486f281ea674e4f69ec989e2b
http://arxiv.org/abs/2007.08326

ON THE ITERATIVE SOLUTION OF SYSTEMS OF THE FORM A T Ax = A T b + c

Autor: Henri Calandra, Serge Gratton, Elisa Riccietti, Xavier Vasseur

Publikováno v: SIAM Journal on Matrix Analysis and Applications
SIAM Journal on Matrix Analysis and Applications, Society for Industrial and Applied Mathematics, 2020, pp.1-25
HAL
SIAM Journal on Matrix Analysis and Applications, 2020, pp.1-25

International audience; Given a full column rank matrix A ∈ R m×n (m ≥ n), we consider a special class of linear systems of the form A ⊤ Ax = A ⊤ b + c with x, c ∈ R n and b ∈ R m. The occurrence of c in the right-hand side of the equati

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=dedup_wf_001::c9471471dc76f8a53f64d66b9fb6f7a6
https://hal.archives-ouvertes.fr/hal-02943217

Modelling spatially correlated observation errors in variational data assimilation using a diffusion operator on an unstructured mesh

Autor: Anthony T. Weaver, Xavier Vasseur, Selime Gürol, Serge Gratton, Yann Michel, Oliver Guillet

Publikováno v: Quarterly Journal of the Royal Meteorological Society
Quarterly Journal of the Royal Meteorological Society, Wiley, 2019, pp.1-21. ⟨10.1002/qj.3537⟩
Quarterly Journal of the Royal Meteorological Society, 2019, pp.1-21. ⟨10.1002/qj.3537⟩

International audience; We propose a method for representing spatially correlated observation errors in variational data assimilation. The method is based on the numerical solution of a diffusion equation, a technique commonly used for representing s

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::bf1da7a78496a8eab11039fb7082154a
https://hal.archives-ouvertes.fr/hal-02160404

Limited memory preconditioners for symmetric indefinite problems with application to structural mechanics

Autor: Sylvain Mercier, Xavier Vasseur, Nicolas Tardieu, Serge Gratton

Publikováno v: Numerical Linear Algebra with Applications. 23:865-887

Summary This paper presents a class of limited memory preconditioners (LMP) for solving linear systems of equations with symmetric indefinite matrices and multiple right-hand sides. These preconditioners based on limited memory quasi-Newton formulas

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_________::8c3806a850703ac7c0ea8d0a42f28adc
https://doi.org/10.1002/nla.2058