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Solving large systems of polynomial equations by using multi linear algebra tool...

Solving large systems of polynomial equations by using multi linear algebra tools The modelling of real-life nonlinear processes is commonly done via local linearization, i.e., by fitting linear models to small ranges of the process. Linearization is, however, quite limited in range and model properties. A fo... ver más

01/03/2020

KU Leuven

161K€

Presupuesto del proyecto: 161K€

Líder del proyecto

KATHOLIEKE UNIVERSITEIT LEUVEN No se ha especificado una descripción o un objeto social para esta compañía.

TRL 4-5

Fecha límite participación Sin fecha límite de participación.

Financiación concedida El organismo H2020 notifico la concesión del proyecto el día 2020-03-01

MSCA-IF-2016: Individual Fellowships

I+D

Cerrada hace 8 años

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No hay información privada compartida para este proyecto. Habla con el coordinador.

1 Participantes

KU Leuven

160.80K€ | Lider

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Duración del proyecto: 35 meses Fecha Inicio: 2017-03-17
Fecha Fin: 2020-03-01

Líder del proyecto

KATHOLIEKE UNIVERSITEIT LEUVEN No se ha especificado una descripción o un objeto social para esta compañía.

TRL 4-5

Presupuesto del proyecto 161K€

Fecha límite de participación Sin fecha límite de participación.

Descripción del proyecto The modelling of real-life nonlinear processes is commonly done via local linearization, i.e., by fitting linear models to small ranges of the process. Linearization is, however, quite limited in range and model properties. A foundational step is currently being made by moving from linear to multi-linear or polynomial models to capture more general features of a nonlinear process over larger ranges. A second important development is Big Data: nowadays we often encounter high-dimensional datasets with multiple `independent’ modes of variation. This increases the numbers of equations and variables and the degrees of the polynomials in the multi-linear models that are required. Big Data research is a key priority in the EU Horizon 2020 Work Programme. This proposal joins both the cutting edge multi-linear and Big Data developments and as a next step aims to develop new robust and efficient numerical methods to solve large polynomial systems. Polynomial equations arise naturally in a large number of diverse fields such as signal processing, robotics, coding theory, optimization, bioinformatics, computer vision, game theory, statistics, machine learning, and systems and control theory. In many applications the coefficients of the polynomials are noisy (i.e., computed from measured data). Currently, solving polynomial equations is commonly done via ‘symbolic algebra’ tools, but these are not suitable for equations with noisy coefficients. However, the rediscovered work of Sylvester and Macaulay puts the problem in a linear algebra setting and well-known numerical linear algebra tools can be used. This project will go beyond this and uses new highly efficient multi-linear algebra tools in the field of tensor decompositions. The latter are higher-order generalizations of the matrix singular valued decomposition. The project combines polynomial algebra, numerical linear algebra, and multi-linear algebra, and will have large impact on a large number of applications.

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