Geometric Inexact Newton Method for Generalized Singular Values of Grassmann Matrix Pair

Wei Wei Xu; Michael K. Ng; Zheng Jian Bai

doi:10.1137/20M1383720

Geometric Inexact Newton Method for Generalized Singular Values of Grassmann Matrix Pair

Wei Wei Xu, Michael K. Ng, Zheng Jian Bai^*

^*Corresponding author for this work

Department of Mathematics

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

2 Citations (Scopus)

Abstract

In this paper, we first give new model formulations for computing arbitrary generalized singular value of a Grassmann matrix pair or a real matrix pair. In these new formulations, we need to solve matrix optimization problems with unitary constraints or orthogonal constraints. We propose a geometric inexact Newton-conjugate gradient (Newton-CG) method for solving the resulting matrix optimization problems. Under some mild assumptions, we establish the global and quadratic convergence of the proposed method for the complex case. Some numerical examples are given to illustrate the effectiveness and high accuracy of the proposed method.

Original language	English
Pages (from-to)	535-560
Number of pages	26
Journal	SIAM Journal on Matrix Analysis and Applications
Volume	43
Issue number	2
DOIs	https://doi.org/10.1137/20M1383720
Publication status	Published - Apr 2022

Scopus Subject Areas

Analysis

User-Defined Keywords

arbitrary generalized singular value
Grassmann manifold
Grassmann matrix pair
new model formulation
Riemannian inexact Newton-CG method
Stiefel manifold

UN SDGs

This output contributes to the following UN Sustainable Development Goals (SDGs)

Access to Document

10.1137/20M1383720

Cite this

@article{fd6b61c3fb9348ed88f13ca8c0b424c6,

title = "Geometric Inexact Newton Method for Generalized Singular Values of Grassmann Matrix Pair",

abstract = "In this paper, we first give new model formulations for computing arbitrary generalized singular value of a Grassmann matrix pair or a real matrix pair. In these new formulations, we need to solve matrix optimization problems with unitary constraints or orthogonal constraints. We propose a geometric inexact Newton-conjugate gradient (Newton-CG) method for solving the resulting matrix optimization problems. Under some mild assumptions, we establish the global and quadratic convergence of the proposed method for the complex case. Some numerical examples are given to illustrate the effectiveness and high accuracy of the proposed method.",

keywords = "arbitrary generalized singular value, Grassmann manifold, Grassmann matrix pair, new model formulation, Riemannian inexact Newton-CG method, Stiefel manifold",

author = "Xu, {Wei Wei} and Ng, {Michael K.} and Bai, {Zheng Jian}",

note = "Publisher Copyright: {\textcopyright} 2022 Society for Industrial and Applied Mathematics",

year = "2022",

month = apr,

doi = "10.1137/20M1383720",

language = "English",

volume = "43",

pages = "535--560",

journal = "SIAM Journal on Matrix Analysis and Applications",

issn = "0895-4798",

publisher = "Society for Industrial and Applied Mathematics (SIAM)",

number = "2",

}

TY - JOUR

T1 - Geometric Inexact Newton Method for Generalized Singular Values of Grassmann Matrix Pair

AU - Xu, Wei Wei

AU - Ng, Michael K.

AU - Bai, Zheng Jian

PY - 2022/4

Y1 - 2022/4

N2 - In this paper, we first give new model formulations for computing arbitrary generalized singular value of a Grassmann matrix pair or a real matrix pair. In these new formulations, we need to solve matrix optimization problems with unitary constraints or orthogonal constraints. We propose a geometric inexact Newton-conjugate gradient (Newton-CG) method for solving the resulting matrix optimization problems. Under some mild assumptions, we establish the global and quadratic convergence of the proposed method for the complex case. Some numerical examples are given to illustrate the effectiveness and high accuracy of the proposed method.

AB - In this paper, we first give new model formulations for computing arbitrary generalized singular value of a Grassmann matrix pair or a real matrix pair. In these new formulations, we need to solve matrix optimization problems with unitary constraints or orthogonal constraints. We propose a geometric inexact Newton-conjugate gradient (Newton-CG) method for solving the resulting matrix optimization problems. Under some mild assumptions, we establish the global and quadratic convergence of the proposed method for the complex case. Some numerical examples are given to illustrate the effectiveness and high accuracy of the proposed method.

KW - arbitrary generalized singular value

KW - Grassmann manifold

KW - Grassmann matrix pair

KW - new model formulation

KW - Riemannian inexact Newton-CG method

KW - Stiefel manifold

UR - http://www.scopus.com/inward/record.url?scp=85130604198&partnerID=8YFLogxK

UR - https://epubs.siam.org/doi/10.1137/20M1383720

U2 - 10.1137/20M1383720

DO - 10.1137/20M1383720

M3 - Journal article

AN - SCOPUS:85130604198

SN - 0895-4798

VL - 43

SP - 535

EP - 560

JO - SIAM Journal on Matrix Analysis and Applications

JF - SIAM Journal on Matrix Analysis and Applications

IS - 2

ER -

Geometric Inexact Newton Method for Generalized Singular Values of Grassmann Matrix Pair

Abstract

Scopus Subject Areas

User-Defined Keywords

UN SDGs

Access to Document

Other files and links

Fingerprint

Cite this