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Convergence of generalized inverses and spline projectors. (English) Zbl 0519.41016


MSC:

41A15 Spline approximation
47A05 General (adjoints, conjugates, products, inverses, domains, ranges, etc.)
41A65 Abstract approximation theory (approximation in normed linear spaces and other abstract spaces)
15A09 Theory of matrix inversion and generalized inverses
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References:

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[2] Ben-Israel, A; Greville, T.N, Generalized inverses: theory and applications, (1974), Wiley New York · Zbl 0305.15001
[3] de Boor, C, Convergence of abstract splines, J. approx. theory, 31, 80-89, (1981) · Zbl 0477.41012
[4] {\scR. E. Chang}, The generalized inverses and interpolation theory, in “Recent Applications of Generalized Inverses” (S. L. Campbell, Ed.), Pitman, New York, in press.
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[10] Izumino, S, The product of operators with closed range and an extension of the reverse order law, Tôhoku math. J., 34, 43-52, (1982) · Zbl 0481.47001
[11] ()
[12] Nashed, M.Z, Perturbations and approximations for generalized inverses and linear operator equations, (), 325-396 · Zbl 0633.47001
[13] Shekhtman, B, Unconditional convergence of abstract splines, J. approx. theory, 30, 237-246, (1980) · Zbl 0491.41016
[14] Stewart, G.W, On the perturbations of pseudo-inverses, projections, and linear squares problems, SIAM rev., 19, 634-662, (1977) · Zbl 0379.65021
[15] Wedin, P.-Å, Perturbation theory for pseudo-inverses, Bit, 13, 217-231, (1973) · Zbl 0263.65047
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