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A unified approach to generalized inverses of linear operators: II. Extremal and proximal properties
Authors:
M. Z. Nashed and G. F. Votruba
Journal:
Bull. Amer. Math. Soc. 80 (1974), 831-835
MSC (1970):
Primary 47A50, 47A99, 41A50; Secondary 54C60, 54C65
Part I:
Bull. Amer. Math. Soc., Volume 80, Number 5 (1974), 825--830
MathSciNet review:
0365191
Full-text PDF
References |
Similar Articles |
Additional Information
- 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.
- 2.
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 0310680
(46 #9778)
- 3.
Richard
B. Holmes, A course on optimization and best approximation,
Lecture Notes in Mathematics, Vol. 257, Springer-Verlag, Berlin, 1972. MR 0420367
(54 #8381)
- 4.
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
(43 #1003)
- 5.
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 0365190
(51 #1443), http://dx.doi.org/10.1090/S0002-9904-1974-13527-5
- 6.
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 0255559
(41 #220)
- 7.
R.
Penrose, On best approximation solutions of linear matrix
equations, Proc. Cambridge Philos. Soc. 52 (1956),
17–19. MR
0074092 (17,536d)
- 8.
C.
Radhakrishna Rao and Sujit
Kumar Mitra, Generalized inverse of matrices and its
applications, John Wiley\thinspace&\thinspace Sons, Inc., New
York-London-Sydney, 1971. MR 0338013
(49 #2780)
- 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.
- 2.
- I. Erdelyi 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
- 3.
- R. B. Holmes, A course on optimization and best approximation, Lecture Notes in Math., vol. 257, Springer-Verlag, Berlin, 1972. MR 420367
- 4.
- 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 43 #1003. MR 275246
- 5.
- 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
- 6.
- 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 41 #220. MR 255559
- 7.
- R. Penrose, On best approximate solutions of linear matrix equations, Proc. Cambridge Philos. Soc. 52 (1956), 17-19. MR 17, 536. MR 74092
- 8.
- C. R. Rao and S. K. Mitra, Generalized inverse of matrices and its applications, Wiley, New York, 1971. MR 338013
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Additional Information
DOI:
http://dx.doi.org/10.1090/S0002-9904-1974-13529-9
PII:
S 0002-9904(1974)13529-9
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