Spherical optimization with complex variablesfor computing US-eigenpairs

Guyan Ni () and Minru Bai
Additional contact information
Guyan Ni: National University of Defense Technology
Minru Bai: Hunan University

Computational Optimization and Applications, 2016, vol. 65, issue 3, No 11, 799-820

Abstract: Abstract The aim of this paper is to compute unitary symmetric eigenpairs (US-eigenpairs) of high-order symmetric complex tensors, which is closely related to the best complex rank-one approximation of a symmetric complex tensor and quantum entanglement. It is also an optimization problem of real-valued functions with complex variables. We study the spherical optimization problem with complex variables including the first-order and the second-order Taylor polynomials, optimization conditions and convex functions of real-valued functions with complex variables. We propose an algorithm and show that it is guaranteed to approximate a US-eigenpair of a symmetric complex tensor. Moreover, if the number of US-eigenpair is finite, then the algorithm is convergent to a US-eigenpair. Numerical examples are presented to demonstrate the effectiveness of the proposed method in finding US-eigenpairs.

Keywords: Symmetric complex tensor; Rank-one approximation; US-eigenpair; Z-eigenpair; High-order power method; Quantum entanglement; Optimization with complex variables; 15A18; 15A69; 81P40 (search for similar items in EconPapers)
Date: 2016
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (2)

Downloads: (external link)
http://link.springer.com/10.1007/s10589-016-9848-7 Abstract (text/html)
Access to the full text of the articles in this series is restricted.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:coopap:v:65:y:2016:i:3:d:10.1007_s10589-016-9848-7

Ordering information: This journal article can be ordered from
http://www.springer.com/math/journal/10589

DOI: 10.1007/s10589-016-9848-7

Access Statistics for this article

Computational Optimization and Applications is currently edited by William W. Hager

More articles in Computational Optimization and Applications from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().