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Akademický článek

Quasi-static ensemble variational data assimilation: a theoretical and numerical study with the iterative ensemble Kalman smoother

Autor: A. Fillion, M. Bocquet, S. Gratton

Publikováno v: Nonlinear Processes in Geophysics, Vol 25, Pp 315-334 (2018)

The analysis in nonlinear variational data assimilation is the solution of a non-quadratic minimization. Thus, the analysis efficiency relies on its ability to locate a global minimum of the cost function. If this minimization uses a Gauss–Newto

Externí odkaz: https://doaj.org/article/b0d0ec4fd01c4246bd6388c6fbf605ae

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Akademický článek

Hybrid Levenberg–Marquardt and weak-constraint ensemble Kalman smoother method

Autor: J. Mandel, E. Bergou, S. Gürol, S. Gratton, I. Kasanický

Publikováno v: Nonlinear Processes in Geophysics, Vol 23, Iss 2, Pp 59-73 (2016)

The ensemble Kalman smoother (EnKS) is used as a linear least-squares solver in the Gauss–Newton method for the large nonlinear least-squares system in incremental 4DVAR. The ensemble approach is naturally parallel over the ensemble members and no

Externí odkaz: https://doaj.org/article/d678fdbd426043ed975a50bad923eac0

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Akademický článek

An Explicit Jordan Decomposition of Companion Matrices

Autor: F.S.V. Bazán, S. Gratton

Publikováno v: Trends in Computational and Applied Mathematics, Vol 7, Iss 2 (2006)

We derive a closed form for the Jordan decomposition of companion matrices including properties of generalized eigenvectors. As a consequence, we provide a formula for the inverse of confluent Vandermonde matrices and results on sensitivity of multip

Externí odkaz: https://doaj.org/article/318fbbc5e7f34d9da326d89f669072b0

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Akademický článek

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Adaptive regularization minimization algorithms with nonsmooth norms

Autor: S Gratton, Ph L Toint

Publikováno v: IMA Journal of Numerical Analysis. 43:920-949

An adaptive regularization algorithm (AR$1p$GN) for unconstrained nonlinear minimization is considered, which uses a model consisting of a Taylor expansion of arbitrary degree and regularization term involving a possibly nonsmooth norm. It is shown t

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_________::eccabb29e41b35e949db2eaeef0c987d
https://doi.org/10.1093/imanum/drac005

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OFFO minimization algorithms for second-order optimality and their complexity

Autor: S. Gratton, Ph. L. Toint

Publikováno v: Gratton, S & TOINT, P 2023, ' OFFO minimization algorithms for second-order optimality and their complexity ', Computational Optimization and Applications, vol. 84, no. 2, pp. 573-607 . https://doi.org/10.1007/s10589-022-00435-2
TOINT, P & Gratton, S 2022 ' OFFO minimization algorithms for second-order optimality and their complexity ' .

An Adagrad-inspired class of algorithms for smooth unconstrained optimizationis presented in which the objective function is never evaluated and yet thegradient norms decrease at least as fast as lO(1/\sqrt{k+1}) whilesecond-order optimality measures

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::7e8c338682ed5a1b146ed93339d6a9d6
https://hal.science/hal-03806600

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