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An efficient Krylov subspace algorithm for computing actions of the $\varphi$ matrix function for large matrices is proposed. This matrix function is widely used in exponential time integration, Markov chains and network analysis and many…

Numerical Analysis · Mathematics 2020-10-20 Mike A. Botchev , Leonid A. Knizhnerman , Eugene E. Tyrtyshnikov

The convergence analysis for least-squares finite element methods led to various adaptive mesh-refinement strategies: Collective marking algorithms driven by the built-in a posteriori error estimator or an alternative explicit…

Numerical Analysis · Mathematics 2023-09-18 Philipp Bringmann

For compact self-adjoint operators in Hilbert spaces, two algorithms are proposed to provide fully computable a posteriori error estimate for eigenfunction approximation. Both algorithms apply well to the case of tight clusters and multiple…

Numerical Analysis · Mathematics 2022-07-19 Xuefeng Liu , Tomáš Vejchodský

In this paper, error estimates are presented for a certain class of optimal control problems with elliptic PDE-constraints. It is assumed that in the cost functional the state is measured in terms of the energy norm generated by the state…

Numerical Analysis · Mathematics 2014-10-31 Olli Mali

This paper is concerned with the derivation of conforming and non-conforming functional a posteriori error estimates for elliptic boundary value problems in exterior domains. These estimates provide computable and guaranteed upper and lower…

Numerical Analysis · Mathematics 2014-07-22 Olli Mali , Alexey Muzalevskiy , Dirk Pauly

The theory of evolutionary computation for discrete search spaces has made significant progress in the last ten years. This survey summarizes some of the most important recent results in this research area. It discusses fine-grained models…

Neural and Evolutionary Computing · Computer Science 2021-11-01 Benjamin Doerr , Frank Neumann

The population-based optimization algorithms have provided promising results in feature selection problems. However, the main challenges are high time complexity. Moreover, the interaction between features is another big challenge in FS…

Neural and Evolutionary Computing · Computer Science 2021-10-26 Motahare Namakin , Modjtaba Rouhani , Mostafa Sabzekar

In this work, we apply multi-goal oriented error estimation to the finite element method. In particular, we use the dual weighted residual method and apply it to a model problem. This model problem consist of locally different coercive…

Numerical Analysis · Mathematics 2024-05-30 Bernhard Endtmayer

We provide a posteriori error estimates in the $L^\infty(L^2)-$norm for relaxation time discrete and fully discrete schemes for a class of evolution nonlinear Schr\"odinger equations up to the critical exponent. In particular for the…

Numerical Analysis · Mathematics 2016-05-24 Theodoros Katsaounis , Irene Kyza

We present a new method for proving lower bounds on the expected running time of evolutionary algorithms. It is based on fitness-level partitions and an additional condition on transition probabilities between fitness levels. The method is…

Neural and Evolutionary Computing · Computer Science 2015-03-19 Dirk Sudholt

In the first part of this paper we introduced an algorithm that uses reachable set approximation to approximate the minimum time function of linear control problems. To illustrate the error estimates and to demonstrate differences to other…

Optimization and Control · Mathematics 2016-01-01 Robert Baier , Thuy Thi Thien Le

We derive optimal order a posteriori error estimates for fully discrete approximations of the initial-boundary value problem for the heat equation. For the discretization in time we apply the fractional-step $\vartheta$-scheme and for the…

Numerical Analysis · Mathematics 2014-04-03 Karakatsani Fotini

This work introduces a time-adaptive strategy that uses a refinement estimator based on the first Frenet curvature. In dynamics, a time-adaptive strategy is a mechanism that interactively proposes changes to the time step used in iterative…

Numerical Analysis · Computer Science 2013-05-30 E. N. Lages , E. S. S. Silveira , D. T. Cintra , A. C. Frery

Based on the auxiliary subspace techniques, a hierarchical basis a posteriori error estimator is proposed for the Stokes problem in two and three dimensions. For the error estimator, we need to solve only two global diagonal linear systems…

Numerical Analysis · Mathematics 2023-03-22 Jiachuan Zhang , Ran Zhang , Xiaoshen Wang

Error control by means of a posteriori error estimators or indica-tors and adaptive discretizations, such as adaptive mesh refinement, have emerged in the late seventies. Since then, numerous theoretical developments and improvements have…

Numerical Analysis · Mathematics 2024-07-11 Roland Becker , Stéphane P. A. Bordas , Franz Chouly , Pascal Omnes

This study presents incremental correction methods for refining neural network parameters or control functions entering into a continuous-time dynamic system to achieve improved solution accuracy in satisfying the interim point constraints…

Optimization and Control · Mathematics 2024-03-12 Namhoon Cho , Hyo-Sang Shin , Antonios Tsourdos , Davide Amato

We consider the unilateral contact problem between an elastic body and a rigid foundation in a description that includes both Tresca and Coulomb friction conditions. For this problem, we present an a posteriori error analysis based on an…

Numerical Analysis · Mathematics 2024-01-08 Ilaria Fontana , Daniele A. Di Pietro

We define an a posteriori verification procedure that enables to control and certify PGD-based model reduction techniques applied to parametrized linear elliptic or parabolic problems. Using the concept of constitutive relation error, it…

Numerical Analysis · Mathematics 2018-06-22 Ludovic Chamoin , Florent Pled , Pierre-Eric Allier , Pierre Ladevèze

We design and analyze a posteriori error estimators for the Stokes system with singular sources in suitable $\mathbf{W}^{1,p}\times \mathrm{L}^p$ spaces. We consider classical low-order inf-sup stable and stabilized finite element…

Numerical Analysis · Mathematics 2019-12-19 Francisco Fuica , Felipe Lepe , Enrique Otarola , Daniel Quero

We analyze an algorithm for assigning weights prior to scalarization in discrete multi-objective problems arising from data analysis. The algorithm evolves weights (interpreted as the relevance of features) by a replicator-type dynamic on…

Optimization and Control · Mathematics 2026-05-08 Aris Daniilidis , Alberto Domínguez Corella , Philipp Wissgott