Open AccessCriteria for H-Matrices Based on γ−Diagonally Dominant Matrix
Author(s) -
Xin Li,
Mei Qin
Publication year - 2019
Publication title -
journal of mathematics research
Language(s) - English
Resource type - Journals
eISSN - 1916-9809
pISSN - 1916-9795
DOI - 10.5539/jmr.v11n6p1
Subject(s) - diagonally dominant matrix , mathematics , diagonal , matrix (chemical analysis) , diagonal matrix , main diagonal , matrix splitting , principal (computer security) , band matrix , block matrix , order (exchange) , square matrix , combinatorics , algebra over a field , pure mathematics , symmetric matrix , geometry , computer science , eigenvalues and eigenvectors , materials science , composite material , invertible matrix , operating system , physics , quantum mechanics , finance , economics
In this paper, we present a new practical criteria for H-matrix based on γ-diagonally dominant matrix. In order to make the judgment conditions convenient and effective, we give two new definitions, one is called strong and weak diagonally dominant degree, the other is called the sum of non-principal diagonal element for the matrix. Further, we obtain a new practical method for the determination of the H-matrix by combining the properties of γ-diagonally dominant matrix, constructing positive diagonal matrix, and adding the appropriate parameters. Finally, we offer numerical examples to verify the validity of the judgment conditions, corresponding numerical examples compared the new criteria and the existing results are presented to verify the advantages of the new determination method.