Proper splittings and reduced solutions of matrix equations

Abstract Consider an ordered Banach space and f,g two self-operators defined on the interior of its positive cone. In this article, we prove that the equation f(X)=g(X) has a positive solution, whenever f is strictly \alpha -concave g-monotone or strictly (-\alpha ) -convex g-antitone with g super-homogeneous and surjective. As applications, we show the existence of positive definite solutions to new classes of nonlinear matrix equations.

Download Full-text

Iterative solution to a class of complex matrix equations and its application in time-varying linear system

Journal of Applied Mathematics and Computing ◽

10.1007/s12190-020-01486-6 ◽

2021 ◽

Author(s):

Wenli Wang ◽

Caiqin Song ◽

Shipu Ji

Keyword(s):

Linear System ◽

Iterative Solution ◽

Time Varying ◽

Matrix Equations ◽

Complex Matrix

Download Full-text

Decoupled low-rank iterative methods for a large-scale system of nonlinear matrix equations arising from electron transport of nano materials

Journal of Computational and Applied Mathematics ◽

10.1016/j.cam.2021.113444 ◽

2021 ◽

Vol 392 ◽

pp. 113444

Author(s):

Ning Dong ◽

Bo Yu ◽

Zhao-Yun Meng

Keyword(s):

Electron Transport ◽

Iterative Methods ◽

Large Scale ◽

Low Rank ◽

Matrix Equations ◽

Nano Materials ◽

Large Scale System ◽

Nonlinear Matrix

Download Full-text

USE OF RIGID REFLECTORS FOR THE VIRTUAL INCREASE OF FIELD DATA IN THE NEAR-FIELD ACOUSTICAL HOLOGRAPHY

Journal of Computational Acoustics ◽

10.1142/s0218396x07003202 ◽

2007 ◽

Vol 15 (01) ◽

pp. 49-61 ◽

Cited By ~ 1

Author(s):

SUNG-IL KIM ◽

JEONG-GUON IH ◽

JI-HOON JEONG

Keyword(s):

Boundary Element Method ◽

Transfer Matrix ◽

Field Data ◽

Near Field ◽

Measurement Data ◽

Source Reconstruction ◽

Matrix Equations ◽

Inverse Boundary ◽

Additional Information ◽

Acoustical Holography

This paper suggests the use of rigid reflectors to provide additional information for source reconstruction in near-field acoustical holography based on the inverse boundary element method. The additional field pressure and transfer matrix equations introduced provide a virtual increase in the measurement data without increasing the number of sensors or altering their arrangement, which could cost more than using reflectors. In order to validate this method, we successfully reconstruct a vibrating ellipse.

Download Full-text