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• W1140887656 abstract "Abstract The ability to determine enclosures for the image set of nonlinear functions is pivotal to many applications in engineering. This paper presents a method for the systematic construction of ellipsoidal extensions of factorable functions. It proceeds by lifting the ellipsoid to a higher dimensional space for every atom operation in the function’s directed acyclic graph, thereby accounting for dependencies. We present theoretical results regarding the quadratic Hausdorff convergence of the computed enclosures. Moreover, we propose an efficient implementation, whereby the shape matrix of the lifted ellipsoid is stored in sparse format, and every atom operation corresponds to a sparse update in that matrix. We illustrate these developments with two numerical examples." @default.
• W1140887656 created "2016-06-24" @default.
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• W1140887656 date "2015-01-01" @default.
• W1140887656 modified "2023-10-10" @default.
• W1140887656 title "Ellipsoidal Arithmetic for Multivariate Systems" @default.
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• W1140887656 doi "https://doi.org/10.1016/b978-0-444-63578-5.50123-7" @default.
• W1140887656 hasPublicationYear "2015" @default.
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