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Project

Low rank tensor approximation techniques for up- and downdating of massive online time series clustering

In the MOMENTUM project research teams in Leuven and Lille (France) will study short recurrences for rational Krylov and orthogonal rational functions inspired by studying modified moments matrices. This will lead to new theory and algorithms for computing short recurrences. The theoretical envisaged enrichment is a thorough analysis of the displacement structure of the associated modified Gramians providing new (coupled) recurrences of the associated orthogonal functions or vectors, whose coefficients will be stored efficiently in factored structured rank matrices. Practically we focus on two types of algorithms. First we study how to fastly and reliably building the recurrences including block Krylov and lookahead stabilizing techniques. Second we develop algorithms for inverse eigenvalue problems to retrieve the recurrences linked to a basis (bi-)orthogonal for a pre-defined inner product. These algorithms will be tested on applications related to model order reduction, matrix functions, and robust rational interpolation for identification. Dutch version In dit project, MOMENTUM genaamd, ontwikkelen onderzoeksteam

Date:1 Jan 2023 →  Today
Keywords:rank structured matrices, displacement rank matrices, rational krylov
Disciplines:Numerical analysis