Announcements

MATHEMATICS SEMINAR by Muzaffer Ayvaz

Author: COLLEGE OF SCIENCES
Time: 10:00
Location: SCI 103

KOÇ UNIVERSITY MATHEMATICS SEMINAR
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Speaker          :  Muzaffer Ayvaz, Ph.D., Computational Scientist
Title                :  A Multilinear Rayleigh Quotient Iteration for All Eigenpairs of Symmetric Tensors

Date                : January 16, 2019, Wednesday
Time               : 10:00
Cookie&Tea  : SCI 103 09:45
Place               : SCI 103

Abstract         :  

The symmetric eigenvalue problem is one of the central 

problems of multilinear algebra. It finds applications 

in diverse areas such as magnetic resonance imaging (MRI), 

diffusion kurtosis imaging (DKI), chemometrics, molecular 

conformation, blind source separation, independent component 

analysis.

 

This study extends the concept of inverse iteration with 

Rayleigh quotient for matrices to the symmetric tensors 

(multi-way arrays) for the z-eigenvalue problem. It shows that, 

while multilinear Rayleigh quotient iteration is capable of finding both stable 

and unstable eigenpairs, it also preserves most of its important 

properties, such as local cubic convergence for symmetric multiway 

arrays just as in the case of symmetric matrices. Numerical 

experiments and comparisons with other methods are presented for 

the demonstration of the effectiveness of the proposed algorithm. 

Its global convergence properties are also discussed.

 

Keywords:

 

Key words. tensor eigenvalues, Z-eigenpairs, tensor eigenpairs, 

Rayleigh Quotient Iteration, Inverse Iteration, Inexact Inverse Iteration

 

AMS subject classifications:  15A18, 15A69