Solving large systems of polynomial equations by using multi-linear algebra tools

Projektinformationen

TENSOROOTS

ID Finanzhilfevereinbarung: 746979

DOI 10.3030/746979

Das Projekt endete am 22 August 2017

EK-Unterschriftsdatum 17 März 2017

Startdatum 1 September 2017

Enddatum 1 März 2020

Finanziert unter

• EXCELLENT SCIENCE - Marie Skłodowska-Curie Actions

Gesamtkosten € 160 800,00

EU-Beitrag € 160 800,00

Koordiniert durch

KATHOLIEKE UNIVERSITEIT LEUVEN
Belgium

Ziel

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.

Wissenschaftliches Gebiet

• natural sciences › mathematics › pure mathematics › algebra › linear algebra
• natural sciences › computer and information sciences › data science › big data
• natural sciences › computer and information sciences › artificial intelligence › computer vision
• natural sciences › mathematics › applied mathematics › game theory
• natural sciences › mathematics › applied mathematics › numerical analysis

Schlüsselbegriffe

• polynomial algebra
• multi-linear algebra
• numerical linear algebra
• tensor decompositions
• signal processing
• systems theory

Programm/Programme

• H2020-EU.1.3. - EXCELLENT SCIENCE - Marie Skłodowska-Curie Actions Main Programme
• H2020-EU.1.3.2. - Nurturing excellence by means of cross-border and cross-sector mobility

Thema/Themen

• MSCA-IF-2016 - Individual Fellowships

Aufforderung zur Vorschlagseinreichung

H2020-MSCA-IF-2016

Finanzierungsplan

MSCA-IF - Marie Skłodowska-Curie Individual Fellowships (IF)

Koordinator

KATHOLIEKE UNIVERSITEIT LEUVEN

• Netto-EU-Beitrag: € 160 800,00
• Adresse: OUDE MARKT 13 ; 3000 Leuven ; Belgien
• Region: Vlaams Gewest › Prov. Vlaams-Brabant › Arr. Leuven
• Aktivitätstyp: Higher or Secondary Education Establishments
• Gesamtkosten: € 160 800,00