NDLI: Inheritance properties and sum-of-squares decomposition of Hankel tensors: theory and algorithms

Please wait, while we are loading the content...

Practical splitting methods for the adaptive integration of nonlinear evolution equations. Part I: Construction of optimized schemes and pairs of schemes

On estimating the separation of two periodic matrix sequences

A convergent finite difference scheme for the Ostrovsky-Hunter equation on a bounded domain

Locally Linearized methods for the simulation of stochastic oscillators driven by random forces

Cheap arbitrary high order methods for single integrand SDEs

Inheritance properties and sum-of-squares decomposition of Hankel tensors: theory and algorithms

Generalized Gauss–Radau and Gauss–Lobatto formulas with Jacobi weight functions

Parameter-uniform numerical methods for general nonlinear singularly perturbed reaction diffusion problems having a stable reduced solution

Efficient weak second-order stochastic Runge–Kutta methods for Itô stochastic differential equations

BIT Numerical Mathematics : Volume 56

BIT Numerical Mathematics : Volume 55

BIT Numerical Mathematics : Volume 54

BIT Numerical Mathematics : Volume 53

BIT Numerical Mathematics : Volume 52

BIT Numerical Mathematics : Volume 51

BIT Numerical Mathematics : Volume 50

BIT Numerical Mathematics : Volume 49

BIT Numerical Mathematics : Volume 48

BIT Numerical Mathematics : Volume 47

BIT Numerical Mathematics : Volume 46

BIT Numerical Mathematics : Volume 45

BIT Numerical Mathematics : Volume 44

BIT Numerical Mathematics : Volume 43

BIT Numerical Mathematics : Volume 42

BIT Numerical Mathematics : Volume 41

BIT Numerical Mathematics : Volume 40

BIT Numerical Mathematics : Volume 39

BIT Numerical Mathematics : Volume 38

BIT Numerical Mathematics : Volume 37

Inheritance properties and sum-of-squares decomposition of Hankel tensors: theory and algorithms

Content Provider	Springer Nature Link
Author	Qi, Liqun Ding, Weiyang Wei, Yimin
Copyright Year	2016
Abstract	In this paper, we show that if a lower-order Hankel tensor is positive semi-definite (or positive definite, or negative semi-definite, or negative definite, or SOS), then its associated higher-order Hankel tensor with the same generating vector, where the higher order is a multiple of the lower order, is also positive semi-definite (or positive definite, or negative semi-definite, or negative definite, or SOS, respectively). Furthermore, in this case, the extremal H-eigenvalues of the higher order tensor are bounded by the extremal H-eigenvalues of the lower order tensor, multiplied with some constants. Based on this inheritance property, we give a concrete sum-of-squares decomposition for each strong Hankel tensor. Then we prove the second inheritance property of Hankel tensors, i.e., a Hankel tensor has no negative (or non-positive, or positive, or nonnegative) H-eigenvalues if the associated Hankel matrix of that Hankel tensor has no negative (or non-positive, or positive, or nonnegative, respectively) eigenvalues. In this case, the extremal H-eigenvalues of the Hankel tensor are also bounded by the extremal eigenvalues of the associated Hankel matrix, multiplied with some constants. The third inheritance property of Hankel tensors is raised as a conjecture.
Ending Page	190
Page Count	22
Starting Page	169
File Format	PDF
ISSN	00063835
e-ISSN	15729125
Journal	BIT Numerical Mathematics
Issue Number	1
Volume Number	57
Language	English
Publisher	Springer Netherlands
Publisher Date	2016-06-06
Publisher Place	Dordrecht
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Eigenvalues, singular values, and eigenvectors Multilinear algebra, tensor products Computational Mathematics and Numerical Analysis Inheritance property Sum-of-squares Convolution Iterative methods for linear systems Hankel tensor Positive semi-definite tensor Numeric Computing Eigenvalues, eigenvectors Mathematics
Content Type	Text
Resource Type	Article
Subject	Applied Mathematics Computer Networks and Communications Computational Mathematics Software

Sl.	Authority	Responsibilities	Communication Details
1	Ministry of Education (GoI), Department of Higher Education	Sanctioning Authority	https://www.education.gov.in/ict-initiatives
2	Indian Institute of Technology Kharagpur	Host Institute of the Project: The host institute of the project is responsible for providing infrastructure support and hosting the project	https://www.iitkgp.ac.in
3	National Digital Library of India Office, Indian Institute of Technology Kharagpur	The administrative and infrastructural headquarters of the project	Dr. B. Sutradhar bsutra@ndl.gov.in
4	Project PI / Joint PI	Principal Investigator and Joint Principal Investigators of the project	Dr. B. Sutradhar bsutra@ndl.gov.in Prof. Saswat Chakrabarti will be added soon
5	Website/Portal (Helpdesk)	Queries regarding NDLI and its services	support@ndl.gov.in
6	Contents and Copyright Issues	Queries related to content curation and copyright issues	content@ndl.gov.in
7	National Digital Library of India Club (NDLI Club)	Queries related to NDLI Club formation, support, user awareness program, seminar/symposium, collaboration, social media, promotion, and outreach	clubsupport@ndl.gov.in
8	Digital Preservation Centre (DPC)	Assistance with digitizing and archiving copyright-free printed books	dpc@ndl.gov.in
9	IDR Setup or Support	Queries related to establishment and support of Institutional Digital Repository (IDR) and IDR workshops	idr@ndl.gov.in

Positive Definite Tensors to Nonlinear Complementarity Problems

Generalized Vandermonde tensors

SOS-Hankel Tensors: Theory and Application

Criteria for strong H-tensors

ℋ-tensors and nonsingular ℋ-tensors

Solving Multilinear Systems via Tensor Inversion

Stochastic $R_0$ Tensors to Stochastic Tensor Complementarity Problems

A Multilinear Singular Value Decomposition

Symmetric Nonnegative Tensors and Copositive Tensors

Inheritance properties and sum-of-squares decomposition of Hankel tensors: theory and algorithms

Similar Documents

Positive Definite Tensors to Nonlinear Complementarity Problems

Generalized Vandermonde tensors

SOS-Hankel Tensors: Theory and Application

Criteria for strong H-tensors

ℋ-tensors and nonsingular ℋ-tensors

Solving Multilinear Systems via Tensor Inversion

Stochastic $R_0$ Tensors to Stochastic Tensor Complementarity Problems

A Multilinear Singular Value Decomposition

Symmetric Nonnegative Tensors and Copositive Tensors

Inheritance properties and sum-of-squares decomposition of Hankel tensors: theory and algorithms