Estimation Of The Correlation Bounds Of Strictly Doubly Diagonally Dominant Matrices

The strictly doubly diagonally dominant matrix is a special type of H-matrix,which has important applications in many fields such as numerical calculation,matrix theory and control theory.In recent years,many scholars at home and abroad have studied strictly diagonally dominant matrix,including its properties and judgments,the upper bound of the infinite norm of its inverse matrix,the lower bound of the minimum eigenvalue and the upper and lower bound of the determinant.Many achievements have been made,but for a wider range of strictly doubly diagonally dominant matrices,the results of research are few,especially the estimation of the correlation boundary is rare.Therefore,the study of strictly doubly diagonally dominant matrix has important theoretical value,and also provides theoretical support for its wide application.Based on the knowledge of the theory of double diagonal dominance,this paper analyzes the relationship between strictly doubly diagonally dominant matrices and strictly diagonally dominant matrices to research the upper and lower bounds of the determinant of strictly doubly diagonally dominant matrices and the upper bound estimation of the infinite norm of inverse matrices.The content mainly includes the following three aspects.Firstly,for the problem of estimating the upper and lower bounds of the determinant of strictly doubly diagonally dominant matrices,multiply the strictly doubly diagonally dominant matrix right by a positive diagonal matrix to make it a strictly diagonally dominant matrix.The upper and lower bounds of the determinant of the strictly diagonally dominant matrix are estimated to obtain a new estimate of the upper and lower bounds of the strictly doubly diagonally dominant matrix determinant.The convergence of the estimated sequence is analyzed,and the results of numerical experiments show its effectiveness,and the obtained estimates improve some existing results.Secondly,by estimating the upper bound of the infinite norm of the inverse matrix of the strictly diagonally dominant M-matrix,a new estimate of the upper bound of the infinite norm of the inverse matrix of the strictly double diagonal dominant M-matrix is obtained.At the same time,a new lower bound of the minimum eigenvalue of the M-matrix is obtained.a convergence analysis is performed,and the numerical experimental results show that the given method is feasible and closer to the true value than some existing results.Finally,based on the estimation of the upper bound of the infinite norm of the inverse matrix of the strictly doubly diagonally dominant M-matrix,the method of matrix splittingis applied to the infinite norm of the inverse matrix of the strict a-double diagonal dominant M-matrix,and get the corresponding estimation sequence under the condition of reduction,and the results of numerical experiments show that the new estimation formula is effective.There are still many issues worthy of study about strictly doubly diagonally dominant matrices.Finally,the paper gives some ideas for further research.