Norm Estimation Of The Moore-Penrose Inverse Of Matrix Multiplication Perturbations

The generalized inverse of matrices are widely used in solving linear equations,opti-mization problems.The multiplicative perturbation of matrices also has important ap-plications in various fields such as the least squares problems,representations for the Moore-Penrose inverse of certain partitioned matrices and so on.Moore-Penrose inverses of multiplication perturbations have various applications,and much effort has been made by many mathematicians.A multiplication perturbation of matrix A?Cm×n has the form of B = D1*AD2,where A is given,D1 and D2 are both invertible,which,can be changed.Let A(?)and B(?)denote the Moore-Penrose inverse of matrices A and B,respectively.One important topic concerning representations for Moore-Penrose inverses is the study of the relationship between B(?)and A(?).In this paper,we deal with norm estimations for the Moore-Penrose inverse associated with Frobenius norm and spectral norm.Many researchers have managed to derive new upper bounds for ?B(?)-A(?)?F and ?B(?)-A(?)?2 by using the Singular Value Decomposition,which serves as the main tool in their paper.Many results can be found in the literatures concerning norm bounds for ?B(?)-A(?)?F and ?B(?)-A(?)?2.We can use the new method to improve relevant results,we divide B(?)-A(?)into three parts,namely,B(?)-A(?)= B(?)AA(?)-B(?)BA(?)+B(?)(Im-AA(?))-(In-B(?)B)A(?).Obviously we have dim(BB(?))= dim(AA(?)),we deal with norm estimation of each part,respectively.By way of introducing parameters and projective decomposition we can get sharper norm upper bounds of ?B(?)-A(?)?F and?B(?)-A(?)?2.