A unified approach to generalized inverses of linear operators: II. Extremal and proximal properties
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- by M. Z. Nashed and G. F. Votruba PDF
- Bull. Amer. Math. Soc. 80 (1974), 831-835
References
-
1. P. J. Erdelsky, Projections in a normed linear space and a generalization of the pseudoinverse, Doctoral Dissertation, California Institute of Technology, Pasadena, Calif., 1969.
- I. Erdélyi and A. Ben-Israel, Extremal solutions of linear equations and generalized inversion between Hilbert spaces, J. Math. Anal. Appl. 39 (1972), 298–313. MR 310680, DOI 10.1016/0022-247X(72)90202-8
- Richard B. Holmes, A course on optimization and best approximation, Lecture Notes in Mathematics, Vol. 257, Springer-Verlag, Berlin-New York, 1972. MR 0420367, DOI 10.1007/BFb0059450
- M. Z. Nashed, Generalized inverses, normal solvability, and iteration for singular operator equations, Nonlinear Functional Anal. and Appl. (Proc. Advanced Sem., Math. Res. Center, Univ. of Wisconsin, Madison, Wis., 1970) Academic Press, New York, 1971, pp. 311–359. MR 0275246
- M. Z. Nashed and G. F. Votruba, A unified approach to generalized inverses of linear operators. I. Algebraic, topological and projectional properties, Bull. Amer. Math. Soc. 80 (1974), 825–830. MR 365190, DOI 10.1090/S0002-9904-1974-13527-5
- T. G. Newman and P. L. Odell, On the concept of a $p-q$ generalized inverse of a matrix, SIAM J. Appl. Math. 17 (1969), 520–525. MR 255559, DOI 10.1137/0117050
- R. Penrose, On best approximation solutions of linear matrix equations, Proc. Cambridge Philos. Soc. 52 (1956), 17–19. MR 74092, DOI 10.1017/S0305004100030929
- C. Radhakrishna Rao and Sujit Kumar Mitra, Generalized inverse of matrices and its applications, John Wiley & Sons, Inc., New York-London-Sydney, 1971. MR 0338013
Additional Information
- Journal: Bull. Amer. Math. Soc. 80 (1974), 831-835
- MSC (1970): Primary 47A50, 47A99, 41A50; Secondary 54C60, 54C65
- DOI: https://doi.org/10.1090/S0002-9904-1974-13529-9
- MathSciNet review: 0365191