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

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.

Ketersediaan

Informasi Detail

Judul Seri

SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS; Vol.43 No.2 April-June 2022

No. Panggil

-

Penerbit

: .,

Deskripsi Fisik

p. 535-560

Bahasa

English

ISBN/ISSN

-

Klasifikasi

NONE

Tipe Isi

-

Tipe Media

-

Tipe Pembawa

-

Edisi

-

Subjek

STIEFEL MANIFOLD
GRASSMANN MANIFOLD
GRASSMANN MATRIX PAIR
NEW MODEL FORMULATION
ARBITRARY GENERALIZED SINGULAR VALUE
RIEMANNIAN INEXACT NEWTON-CG METHOD

Info Detail Spesifik

https://doi.org/10.1137/20M1383720

Pernyataan Tanggungjawab

Wei-Wei Xu, Michael K. Ng, Zheng-Jian Bai

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