On symmetric and skew-symmetric solutions to a procrustes problem

Yuan Bei Deng; Daniel Boley

doi:10.1007/978-94-007-0602-6_11

On symmetric and skew-symmetric solutions to a procrustes problem

Yuan Bei Deng, Daniel Boley

Computer Science and Engineering

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

Abstract

Using the projection theorem in a Hilbert space, the quotient singular value decomposition (QSVD) and the canonical correlation decomposition (CCD) in matrix theory for efficient tools, we obtained the explicit analytical expressions of the optimal approximation solutions for the symmetric and skew-symmetric least-squares problems of the linear matrix equation . This can lead to new algorithms to solve such problems.

Original language	English (US)
Title of host publication	Numerical Linear Algebra in Signals, Systems and Control
Pages	201-215
Number of pages	15
DOIs	https://doi.org/10.1007/978-94-007-0602-6_11
State	Published - 2011
Event	International Workshop on Numerical Linear Algebra in Signal, Systems, and Control - Kharagpur, India Duration: Jan 9 2007 → Jan 11 2007

Publication series

Name	Lecture Notes in Electrical Engineering
Volume	80 LNEE
ISSN (Print)	1876-1100
ISSN (Electronic)	1876-1119

Other

Other	International Workshop on Numerical Linear Algebra in Signal, Systems, and Control
Country/Territory	India
City	Kharagpur
Period	1/9/07 → 1/11/07

Bibliographical note

Funding Information:
The author Deng would like to thank the China Scholarship Council for providing the State Scholarship Fund to pursue his research at the University of Minnesota as a visiting scholar. The author Boley would like to acknowledge partial support for this research from NSF grant IIS-0916750.

Keywords

CCD
Least-squares problem (Procrustes problem)
Linear matrix equation
Optimal approximation solution
QSVD

Access

10.1007/978-94-007-0602-6_11

OpenUrl availability

Full text

Cite this

Deng, YB & Boley, D 2011, On symmetric and skew-symmetric solutions to a procrustes problem. in Numerical Linear Algebra in Signals, Systems and Control. Lecture Notes in Electrical Engineering, vol. 80 LNEE, pp. 201-215, International Workshop on Numerical Linear Algebra in Signal, Systems, and Control, Kharagpur, India, 1/9/07. https://doi.org/10.1007/978-94-007-0602-6_11

@inproceedings{e967ff7b495c4fc8b0441fb6265914e6,

title = "On symmetric and skew-symmetric solutions to a procrustes problem",

abstract = "Using the projection theorem in a Hilbert space, the quotient singular value decomposition (QSVD) and the canonical correlation decomposition (CCD) in matrix theory for efficient tools, we obtained the explicit analytical expressions of the optimal approximation solutions for the symmetric and skew-symmetric least-squares problems of the linear matrix equation . This can lead to new algorithms to solve such problems.",

keywords = "CCD, Least-squares problem (Procrustes problem), Linear matrix equation, Optimal approximation solution, QSVD",

author = "Deng, {Yuan Bei} and Daniel Boley",

note = "Funding Information: The author Deng would like to thank the China Scholarship Council for providing the State Scholarship Fund to pursue his research at the University of Minnesota as a visiting scholar. The author Boley would like to acknowledge partial support for this research from NSF grant IIS-0916750.; International Workshop on Numerical Linear Algebra in Signal, Systems, and Control ; Conference date: 09-01-2007 Through 11-01-2007",

year = "2011",

doi = "10.1007/978-94-007-0602-6_11",

language = "English (US)",

isbn = "9789400706019",

series = "Lecture Notes in Electrical Engineering",

pages = "201--215",

booktitle = "Numerical Linear Algebra in Signals, Systems and Control",

}

TY - GEN

T1 - On symmetric and skew-symmetric solutions to a procrustes problem

AU - Deng, Yuan Bei

AU - Boley, Daniel

N1 - Funding Information: The author Deng would like to thank the China Scholarship Council for providing the State Scholarship Fund to pursue his research at the University of Minnesota as a visiting scholar. The author Boley would like to acknowledge partial support for this research from NSF grant IIS-0916750.

PY - 2011

Y1 - 2011

N2 - Using the projection theorem in a Hilbert space, the quotient singular value decomposition (QSVD) and the canonical correlation decomposition (CCD) in matrix theory for efficient tools, we obtained the explicit analytical expressions of the optimal approximation solutions for the symmetric and skew-symmetric least-squares problems of the linear matrix equation . This can lead to new algorithms to solve such problems.

AB - Using the projection theorem in a Hilbert space, the quotient singular value decomposition (QSVD) and the canonical correlation decomposition (CCD) in matrix theory for efficient tools, we obtained the explicit analytical expressions of the optimal approximation solutions for the symmetric and skew-symmetric least-squares problems of the linear matrix equation . This can lead to new algorithms to solve such problems.

KW - CCD

KW - Least-squares problem (Procrustes problem)

KW - Linear matrix equation

KW - Optimal approximation solution

KW - QSVD

UR - http://www.scopus.com/inward/record.url?scp=79957597872&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=79957597872&partnerID=8YFLogxK

U2 - 10.1007/978-94-007-0602-6_11

DO - 10.1007/978-94-007-0602-6_11

M3 - Conference contribution

AN - SCOPUS:79957597872

SN - 9789400706019

T3 - Lecture Notes in Electrical Engineering

SP - 201

EP - 215

BT - Numerical Linear Algebra in Signals, Systems and Control

T2 - International Workshop on Numerical Linear Algebra in Signal, Systems, and Control

Y2 - 9 January 2007 through 11 January 2007

ER -

On symmetric and skew-symmetric solutions to a procrustes problem

Abstract

Publication series

Other

Bibliographical note

Keywords

Access

OpenUrl availability

Other files and links

Fingerprint

Cite this