Iterative Methods for Computing the Weighted Minkowski Inverses of Matrices in Minkowski Space

Authors: Xiaoji Liu, Yonghui Qin

Abstract:

In this note, we consider a family of iterative formula for computing the weighted Minskowski inverses AM,N in Minskowski space, and give two kinds of iterations and the necessary and sufficient conditions of the convergence of iterations.

Keywords: iterative method, the Minskowski inverse, A

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1076478

References:

[1] J.J. Koliha, A simple proof of the product theorem for EP matrices, Linear Algebra Appl. 294(1999) 213-215.
[2] A.R. Meenakshi, D. Krishnaswamy, Product of range symmetric block matrices in Minskowski space, Bull. Malays. Math. Sci. Soc. (29)(1)(2006) 59-68.
[3] Weiguo Li, Zhi Li, A family of iterative methods for computing the approximate inverse of a square matrix and inner inverse of a non-square matrix, Applied Mathematics and Computation, 215(2010) 3433-3442.
[4] Adem KiliC┬© man, Zeyad Al Zhour, The representation and approximation for the weighted Minkowski inverse in Minkowski space, Math. Comput. Model., 34(2008) 363-371.
[5] Y.Chen. Iterative methods for computing the generalized inverse A (2) T,S of a matrix A
[J]. Applied Mathematics and Computation 233(1996)207- 229.
[6] A. Ben-Israel,T.N.E. Greville. Generalized Inverses: Theory and Applications. Wiley, New York, 1974.
[7] X. Jin, Y. Wei, Numerical Linear Algebra and Its Applications
[M], Science Press, Beijing/New York, 2004.
[8] J.J. Koliha. A simple proof of the product theorem for EP matrices
[J]. Linear Algebra and its Applcation, 294(1999) 213-215.
[9] F.Huang, X.Zhang. An improved Newton iteration for the weighted Moore-Penrose inverse
[J]. Applied Mathematics and Computation 174 (2006)1460C1486.