Titlebook: Numerical Software Verification; 10th International W Alessandro Abate,Sylvie Boldo Conference proceedings 2017 Springer International Publ

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Verified Computations Using Taylor Models and Their Applications arithmetic that is long known for rigorous, verified computations, and all operations are conducted on intervals instead of numbers. However, interval computations suffer from overestimation, the dependency problem, the dimensionality curse, and the wrapping effect, to name a few, and those difficu

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Introduction to the IEEE 1788-2015 Standard for Interval Arithmeticsult is an interval that is guaranteed to contain the exact numerical values, regardless of uncertainty or roundoff errors..From 2008 to 2015, interval arithmetic underwent a standardization effort, resulting in the IEEE 1788-2015 standard. The main features of this standard are developed: the struc

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Studying the Numerical Quality of an Industrial Computing Code: A Case Study on Code_astere. Random rounding, using the Verrou diagnostics tool, is first used to evaluate the numerical stability, and locate the origin of errors in the source code. Once a small code part is identified as unstable, it can be isolated and studied using higher precision computations and interval arithmetic t

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Challenges and Tool Implementation of Hybrid Rapidly-Exploring Random Treese tree is constructed from random points drawn from system’s state space and is biased to grow towards large unexplored areas in the system. RRT can provide better coverage of a system’s possible behaviors compared with random simulations, but is more lightweight than full reachability analysis. In

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Rigorous Reachability Analysis and Domain Decomposition of Taylor Modelsbout their long term evolution. Of particular interest are determination of locations of attractors, reachability of certain sets, and proof of non-reachability of others. The methods are based on Taylor model verified integrators for the propagation of large domains, and heavily rely on automatic d

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A Study of Model-Order Reduction Techniques for Verificationimate models are gaining increasing popularity. Model-order reduction techniques take large ordinary differential equation models and simplify them to yield models that are potentially much smaller in size. These approaches typically discover a suitable projection of the state space into a smaller s

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eve goals and the most efficient process (Kotler and Armstrong 2018). Supply chains consist of individual entities and networks across countries, which are also managed to pursue individual organization revenue goals. Interplay of two cultural orientations is therefore bound to exist naturally in ma

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resorts, ships and hotels. This area is related to the provision of all required facilities to customers, including accommodation and food. In 2015, one in ten enterprises in the European non-financial business economy belonged to the tourism industries. These 2.4 million enterprises employed an est

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Kyoko Makino,Martin Berztment, and laser treatment, are available for treating scars. Assessment of the treatment outcome is crucial for determining appropriate treatment modality. In this chapter, we introduce assessment tools for scars. First, we address subjective assessment using scar rating scales in chronological ord