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A Certified Cubic B-Spline Interpolation Method with Tangential Direction Constraints
Curve interpolation with B-spline is widely used in various areas. This problem is classic and recently raised in application scenario with new...
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An adaptive certified space-time reduced basis method for nonsmooth parabolic partial differential equations
In this paper, a nonsmooth semilinear parabolic partial differential equation (PDE) is considered. For a reduced basis (RB) approach, a space-time...
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Toward a certified greedy Loewner framework with minimal sampling
We propose a strategy for greedy sampling in the context of non-intrusive interpolation-based surrogate modeling for frequency-domain problems. We...
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Efficient and certified solution of parametrized one-way coupled problems through DEIM-based data projection across non-conforming interfaces
One of the major challenges of coupled problems is to manage nonconforming meshes at the interface between two models and/or domains, due to...
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The Frank-Wolfe Algorithm: A Short Introduction
In this paper we provide an introduction to the Frank-Wolfe algorithm, a method for smooth convex optimization in the presence of (relatively)...
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A space-time certified reduced basis method for quasilinear parabolic partial differential equations
In this paper, we propose a certified reduced basis (RB) method for quasilinear parabolic problems with strongly monotone spatial differential...
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A branch-and-cut algorithm for the balanced traveling salesman problem
The balanced traveling salesman problem (BTSP) is a variant of the traveling salesman problem, in which one seeks a tour that minimizes the...
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A Polyhedral Homotopy Algorithm for Real Zeros
We design a homotopy continuation algorithm, that is based on Viro’s patchworking method, for finding real zeros of sparse polynomial systems. The...
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On the Complexity of the Plantinga–Vegter Algorithm
We introduce tools from numerical analysis and high dimensional probability for precision control and complexity analysis of subdivision-based...
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Nonmonotone feasible arc search algorithm for minimization on Stiefel manifold
We devise a new numerical method for solving the minimization problem over the Stiefel manifold, that is, the set of matrices of order
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A branch-and-prune algorithm for discrete Nash equilibrium problems
We present a branch-and-prune procedure for discrete Nash equilibrium problems with a convex description of each player’s strategy set. The derived...
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Certified Efficient Global Roundness Evaluation
We propose and analyze a global search algorithm for the computation of the minimum zone sphericity (circularity) error of a given set. The...
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Certified Machine-Learning Models
The massive adoption of Machine Learning (ML) has deeply changed the internal structure, the design and the operation of software systems. ML has...
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Certified Mapper: Repeated Testing for Acyclicity and Obstructions to the Nerve Lemma
The Mapper algorithm does not include a check for whether the cover produced conforms to the requirements of the nerve lemma. To perform a check for...
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A Symbolic-Numeric Validation Algorithm for Linear ODEs with Newton–Picard Method
A symbolic-numeric validation algorithm is developed to compute rigorous and tight uniform error bounds for polynomial approximate solutions to...
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3D-VAR for parameterized partial differential equations: a certified reduced basis approach
In this paper, we propose a reduced order approach for 3D variational data assimilation governed by parameterized partial differential equations. In...
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An Algorithm Verifying the Congruence of Complex Matrices Whose Cosquares Have Eigenvalues of Modulus One
AbstractA finite computational process using arithmetic operations only is called a rational algorithm. Presently, no rational algorithm is available...
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Adaptive machine learning-based surrogate modeling to accelerate PDE-constrained optimization in enhanced oil recovery
In this contribution, we develop an efficient surrogate modeling framework for simulation-based optimization of enhanced oil recovery, where we...
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On the Spectrum Distribution of Parametric Second-Order Delay Differential Equations: Perspectives in Partial Pole Placement
This chapter presents a parameter-based frequency-domain approach for the analysis and control of linear time-invariant dynamical systems described...
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A rigorous deterministic global optimization approach for the derivation of secondary information in digital maps
We derive a generic system that constructs an optimization model for an emergency stop scenario on the highway, based on map data from high...
