1 IntroductionLet A∈C<sup>n×n</sup>, B∈C<sup>n×n</sup>.We say B is a square root of A if A=B×B i.e.A=B<sup>2</sup>.It is well-known that any symmetric positive defi...1 IntroductionLet A∈C<sup>n×n</sup>, B∈C<sup>n×n</sup>.We say B is a square root of A if A=B×B i.e.A=B<sup>2</sup>.It is well-known that any symmetric positive definite matrix exists one and only onesquare root which is a symmetric positive definite matrix,too（e.g.see[5]）.Higham[4]studied carefully the relation of a real nonsingular matrix between its real square rootsand its eigenvalues.Alefeld and Schneider[1]pointed out that for any nonsingular M-ma-trix there is one and only one M-matrix as its square root.In this paper,we study on展开更多
A direct algorithm is proposed by which one can distinguish whether a matrix is an M-matrix (or H-matrix) or not quickly and effectively. Numerical examples show that it is effective and convincible to distinguish M-m...A direct algorithm is proposed by which one can distinguish whether a matrix is an M-matrix (or H-matrix) or not quickly and effectively. Numerical examples show that it is effective and convincible to distinguish M-matrix (or H-matrix) by using the algorithm.展开更多
基金The second author is supported by Xiamen University,China
文摘1 IntroductionLet A∈C<sup>n×n</sup>, B∈C<sup>n×n</sup>.We say B is a square root of A if A=B×B i.e.A=B<sup>2</sup>.It is well-known that any symmetric positive definite matrix exists one and only onesquare root which is a symmetric positive definite matrix,too（e.g.see[5]）.Higham[4]studied carefully the relation of a real nonsingular matrix between its real square rootsand its eigenvalues.Alefeld and Schneider[1]pointed out that for any nonsingular M-ma-trix there is one and only one M-matrix as its square root.In this paper,we study on
基金Foundation item: This work is supported by the Science Foundations of the Education Department of Yunnan Province (03Z169A)the Science Foundatons of Yunnan University (2003Z013B).
文摘A direct algorithm is proposed by which one can distinguish whether a matrix is an M-matrix (or H-matrix) or not quickly and effectively. Numerical examples show that it is effective and convincible to distinguish M-matrix (or H-matrix) by using the algorithm.
