Text

Systems of Polynomial Equations, Higher-Order Tensor Decompositions, and Multidimensional Harmonic Retrieval : A Unifying Framework. Part II : The Block Term Decomposition

In Part I we proposed a multilinear algebra framework to solve 0-dimensional systems of polynomial equations with simple roots. We extend this framework to incorporate multiple roots: a block term decomposition (BTD) of the null space of the Macaulay matrix reveals the dual (sub)space of a disjoint root in each term. The BTD is the joint triangularization of multiplication tables and a three-way generalization of the Jordan canonical form in the matrix case, intimately related to the border rank of a tensor. We hint at and illustrate flexible numerical optimization-based algorithms.

Ketersediaan

Informasi Detail

Judul Seri

SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS; Vol.42 No.2 April-June 2021

No. Panggil

-

Penerbit

: .,

Deskripsi Fisik

p. 913 - 953

Bahasa

English

ISBN/ISSN

-

Klasifikasi

-

Tipe Isi

-

Tipe Media

-

Tipe Pembawa

-

Edisi

-

Subjek

MULTILINEAR ALGEBRA
BORDER RANK
MACAULAY MATRIX
BLOCK TERM DECOMPOSITION
SYSTEM OF POLYNOMIAL EQUATIONS
MULTIPLICATION TABLE

Info Detail Spesifik

https://doi.org/10.1137/17M1150062

Pernyataan Tanggungjawab

Jeroen Vanderstukken, Patrick Kürschner, Ignat Domanov, Lieven De Lathauwer

Versi lain/terkait

Lampiran Berkas

Komentar