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


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
Full Text: DOI


[1] Anselone, P. M.; Nashed, M. Z., Perturbations of outer inverses, (Cheney, E. W., Approximation Theory III (1980), Academic Press: Academic Press New York/London), 163-168 · Zbl 0476.47007
[2] Ben-Israel, A.; Greville, T. N., Generalized Inverses: Theory and Applications (1974), Wiley: Wiley New York · Zbl 0305.15001
[3] de Boor, C., Convergence of abstract splines, J. Approx. Theory, 31, 80-89 (1981) · Zbl 0477.41012
[5] Delvos, F. J., Splines and pseudoinverses, RAIRO Anal. Numér., 12, 313-324 (1978) · Zbl 0393.65022
[6] Delvos, F. J.; Schempp, W., Optimal approximation and the method of least squares, J. Approx. Theory, 33, 214-223 (1981) · Zbl 0445.41008
[7] Groetsch, C. W., Generalized Inverses of Linear Operators: Representation and Approximation (1977), Dekker: Dekker New York/Basel · Zbl 0358.47001
[8] Groetsch, C. W., Generalized inverses and generalized splines, Numer. Fund. Optim., 2, 1, 93-97 (1980) · Zbl 0456.47003
[9] Holmes, R. B., A Course on Optimization and Best Approximation (1972), Springer-Verlag: Springer-Verlag Berlin/Heidelberg/New York · Zbl 0234.46016
[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] (Nashed, M. Z., Generalized Inverses and Applications (1976), Academic Press: Academic Press New York/London) · Zbl 0324.00009
[12] Nashed, M. Z., Perturbations and Approximations for generalized inverses and linear operator equations, (Nashed, M. Z., Generalized Inverses and Applications (1976), Academic Press: Academic Press New York), 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
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.