A self-correcting matrix iteration for the Moore-Penrose generalized inverse

Linear Algebra and Its Applications

Volumn 244, Issue , 1996, Pages 357-363

  Pierce, William H ^a  

^a University of Louisville ^*  (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0030514770     PISSN: 00243795     EISSN: None     Source Type: Journal    
DOI: 10.1016/0024-3795(94)00306-8     Document Type: Article

References (17)

1. A. S. Householder, The Theory of Matrices in Numerical Analysis, Blaisdell, New York, 1964, Chapter 7.
2. M. Hanke and W. Niethammer, On the acceleration of Kaczmarz's method for inconsistent linear systems, Linear Algebra Appl. 130:83-98 (1990).
3. G. E. Forsythe and C. B. Moler, Computer Solution of Linear Algebraic Systems, Prentice-Hall, Englewood Cliffs, N.J., 1967, Chapters 13, 22.
4. A. Ben-Israel, An iterative method for computing the generalized inverse of an arbitrary matrix, Math. Comp. 19:452-455 (1965).
5. A. Ben-Israel, A note on an iterative method for generalized inversion of matrices, Math. Comp. 20:439-440 (1966).
6. A. Ben-Israel and D. Cohen, On iterative computation of generalized inverses and associated projections, SIAM J. Numer. Anal. 3:410-419 (1966).
7. W. Mönch, Iterative refinement of approximations to a generalized inverse of a matrix, Computing 28:79-87 (1982).
8. W. Mönch, Anwendung des Schulz-Verfahrens zur Nachkorrektur einer näherungsweise Berechneten verallgemeinarten Inversen einer Matrix, Z. Angew. Math. Mech. 61:115-117 (1981).
9. A. K. Katsaggelos and S. N. Efstratiadis, A class of iterative signal restoration algorithms, IEEE Trans. Acoust. Speech Signal Process. 38:778-793 (1990).
10. A. Ben-Israel and T. N. E. Greville, Generalized Inverses: Theory and Applications, Wiley, 1974.
11. T. Söderström and G. W. Stewart, On the numerical properties of an iterative method for computing the Moore-Penrose generalized inverse, SIAM J. Numer. Anal. 11:61-94 (1974).
12. G. Golub and Charles F. Van Loan, Matrix Computations, 2nd ed., Johns Hopkins U. P., Baltimore, 1989.
13. V. Pan and R. Schreiber, An Improved Newton iteration for the generalized inverse of a matrix, with applications, SIAM J. Sci. Statist. Comput. 12(5): 1109-1130 (1991).
14. G. Schulz, Iterative Berechnung der reziproken Matrix, Z. Angew. Math. Mech. 13:57-59 (1933).
15. K. Tanabe, Neumann-type expansion of generalized inverses of a matrix and the hyperpower iterative method, Linear Algebra Appl. 10:163-175 (1975).
16. A. Ben-Israel and A. Chanes, Contributions to the theory of generalized inverses, SIAM J. 11:667-669 (1963).
17. R. D. Skeel, Scaling for numerical stability in Gaussian elimination, J. Assoc. Comput. Mach. 26:494-526 (1979).