Some methods for generating both an NT-net and the uniform distribution on a Stiefel manifold and their applications

Kai-Tai Fang; Run-Ze Li

doi:10.1016/s0167-9473(96)00057-6

Some methods for generating both an NT-net and the uniform distribution on a Stiefel manifold and their applications

Kai-Tai Fang^*, Run-Ze Li

^*Corresponding author for this work

Research output: Contribution to journal › Journal article › peer-review

10 Citations (Scopus)

Abstract

We propose in this paper two methods for generating both an NT-net (see below) and the uniform distribution on a Stiefel manifold O(n,m), where O(n,m) ={H : H is an n×m matrix and H′H =I_m}. One method is based on the Householder transform while another is based on the Givens transform. Some applications of these two algorithms are presented and some numerical comparisons among these methods are given also.

Original language	English
Pages (from-to)	29-46
Number of pages	18
Journal	Computational Statistics and Data Analysis
Volume	24
Issue number	1
DOIs	https://doi.org/10.1016/s0167-9473(96)00057-6
Publication status	Published - 6 Mar 1997
Externally published	Yes

Scopus Subject Areas

Statistics and Probability
Computational Mathematics
Computational Theory and Mathematics
Applied Mathematics

User-Defined Keywords

Givens transform
Householder transform
Number-theoretic method
Spherical distribution
Stiefel manifold
Test of spherical symmetry

Access to Document

10.1016/s0167-9473(96)00057-6

Cite this

@article{7e8f525d115f47a58625121c0a5120b4,

title = "Some methods for generating both an NT-net and the uniform distribution on a Stiefel manifold and their applications",

abstract = "We propose in this paper two methods for generating both an NT-net (see below) and the uniform distribution on a Stiefel manifold O(n,m), where O(n,m) ={H : H is an n×m matrix and H′H =Im}. One method is based on the Householder transform while another is based on the Givens transform. Some applications of these two algorithms are presented and some numerical comparisons among these methods are given also.",

keywords = "Givens transform, Householder transform, Number-theoretic method, Spherical distribution, Stiefel manifold, Test of spherical symmetry",

author = "Kai-Tai Fang and Run-Ze Li",

note = "Funding Information: This work was partially supported by a Hong Kong UGC grant and Chinese Academy of Sciences.",

year = "1997",

month = mar,

day = "6",

doi = "10.1016/s0167-9473(96)00057-6",

language = "English",

volume = "24",

pages = "29--46",

journal = "Computational Statistics and Data Analysis",

issn = "0167-9473",

publisher = "Elsevier",

number = "1",

}

TY - JOUR

T1 - Some methods for generating both an NT-net and the uniform distribution on a Stiefel manifold and their applications

AU - Fang, Kai-Tai

AU - Li, Run-Ze

N1 - Funding Information: This work was partially supported by a Hong Kong UGC grant and Chinese Academy of Sciences.

PY - 1997/3/6

Y1 - 1997/3/6

N2 - We propose in this paper two methods for generating both an NT-net (see below) and the uniform distribution on a Stiefel manifold O(n,m), where O(n,m) ={H : H is an n×m matrix and H′H =Im}. One method is based on the Householder transform while another is based on the Givens transform. Some applications of these two algorithms are presented and some numerical comparisons among these methods are given also.

AB - We propose in this paper two methods for generating both an NT-net (see below) and the uniform distribution on a Stiefel manifold O(n,m), where O(n,m) ={H : H is an n×m matrix and H′H =Im}. One method is based on the Householder transform while another is based on the Givens transform. Some applications of these two algorithms are presented and some numerical comparisons among these methods are given also.

KW - Givens transform

KW - Householder transform

KW - Number-theoretic method

KW - Spherical distribution

KW - Stiefel manifold

KW - Test of spherical symmetry

UR - http://www.scopus.com/inward/record.url?scp=0031555842&partnerID=8YFLogxK

U2 - 10.1016/s0167-9473(96)00057-6

DO - 10.1016/s0167-9473(96)00057-6

M3 - Journal article

AN - SCOPUS:0031555842

SN - 0167-9473

VL - 24

SP - 29

EP - 46

JO - Computational Statistics and Data Analysis

JF - Computational Statistics and Data Analysis

IS - 1

ER -

Some methods for generating both an NT-net and the uniform distribution on a Stiefel manifold and their applications

Abstract

Scopus Subject Areas

User-Defined Keywords

Access to Document

Other files and links

Fingerprint

Cite this