Validated computation of the local truncation error of Runge–Kutta methods with automatic differentiation

Mullier, Olivier; Chapoutot, Alexandre; Sandretto, Julien Alexandre Dit

doi:10.1080/10556788.2018.1459620

Cited by 14 publications

(10 citation statements)

References 23 publications

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“…Starting from the seminal paper of Otter [Ott48], unlabelled tree-like structures play an important role in chemistry, phylogenetics [Pen82] and synthetic biology [FVS17]. Their u 1 z u 2 z u 3 z u 4 z u 5 z u 6 z u 7 z u 8 z u 9 z u 10 z value 0.005 0.015 0.025 0.035 0.044 0.054 0.063 0.072 0.081 0.09 study also helps to discover new methods for numerical solution of partial differential equations, involving automatic differentiation and construction of expression trees [MCA18].…”

Section: Applicationsmentioning

confidence: 99%

Polynomial tuning of multiparametric combinatorial samplers

Bendkowski¹,

Bodini²,

Dovgal³

2018

2018 Proceedings of the Fifteenth Workshop on Analytic Algorithmics and Combinatorics (ANALCO)

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Boltzmann samplers and the recursive method are prominent algorithmic frameworks for the approximate-size and exact-size random generation of large combinatorial structures, such as maps, tilings, RNA sequences or various treelike structures. In their multiparametric variants, these samplers allow to control the profile of expected values corresponding to multiple combinatorial parameters. One can control, for instance, the number of leaves, profile of node degrees in trees or the number of certain subpatterns in strings. However, such a flexible control requires an additional nontrivial tuning procedure. In this paper, we propose an efficient polynomial-time, with respect to the number of tuned parameters, tuning algorithm based on convex optimisation techniques. Finally, we illustrate the efficiency of our approach using several applications of rational, algebraic and Pólya structures including polyomino tilings with prescribed tile frequencies, planar trees with a given specific node degree distribution, and weighted partitions.

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Section: Applicationsmentioning

confidence: 99%

Polynomial tuning of multiparametric combinatorial samplers

Bendkowski¹,

Bodini²,

Dovgal³

2018

2018 Proceedings of the Fifteenth Workshop on Analytic Algorithmics and Combinatorics (ANALCO)

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“…For both examples, Algorithms 1 and 2 were implemented using DynIbex [1] with its improvement described in [16].…”

Section: Numerical Experimentsmentioning

confidence: 99%

Optimal Switching Instants for the Control of Hybrid Systems

2020

Self Cite

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The problem of determining the optimal switching instants for the control of hybrid systems under reachability constraints is considered. This optimization problem is cast into an interval global optimization problem with differential constraints, where validated simulation techniques and a dynamic time meshing are used for the computation of its solution. The approach is applied on two examples, one being the well-known example of the Goddard's problem where a rocket has to reach a given altitude while consuming the smallest amount of fuel, the second one considers a system with an higher dimension and a more complex optimization problem.

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“…Matrices satisfying this non-negativity property for the off-diagonal elements are also denoted as Metzler matrices in the literature [1,5,7,8]. For such systems, general-purpose, interval-based or other set-valued solvers [9] (AWA [10,11], CAPD [12], COSY-VI [13,14], DYNIBEX [15,16], VALENCIA-IVP [17][18][19][20][21], VNODE-LP [22,23], VSPODE [24]) for initial value problems (IVPs) can be replaced by point-valued simulations of a finite number of extremal realizations that can be extracted from the interval box x(0) ∈ [x 0 ] = [x](0) := [x(0) ; x(0)]…”

Section: Introductionmentioning

confidence: 99%

Transformation of Uncertain Linear Systems with Real Eigenvalues into Cooperative Form: The Case of Constant and Time-Varying Bounded Parameters

Rauh

Kersten

2021

Algorithms

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Continuous-time linear systems with uncertain parameters are widely used for modeling real-life processes. The uncertain parameters, contained in the system and input matrices, can be constant or time-varying. In the latter case, they may represent state dependencies of these matrices. Assuming bounded uncertainties, interval methods become applicable for a verified reachability analysis, for feasibility analysis of feedback controllers, or for the design of robust set-valued state estimators. The evaluation of these system models becomes computationally efficient after a transformation into a cooperative state-space representation, where the dynamics satisfy certain monotonicity properties with respect to the initial conditions. To obtain such representations, similarity transformations are required which are not trivial to find for sufficiently wide a-priori bounds of the uncertain parameters. This paper deals with the derivation and algorithmic comparison of two different transformation techniques for which their applicability to processes with constant and time-varying parameters has to be distinguished. An interval-based reachability analysis of the states of a simple electric step-down converter concludes this paper.

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Validated computation of the local truncation error of Runge–Kutta methods with automatic differentiation

Cited by 14 publications

References 23 publications

Polynomial tuning of multiparametric combinatorial samplers

Polynomial tuning of multiparametric combinatorial samplers

Optimal Switching Instants for the Control of Hybrid Systems

Transformation of Uncertain Linear Systems with Real Eigenvalues into Cooperative Form: The Case of Constant and Time-Varying Bounded Parameters

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