Izumino, Saichi Convergence of generalized inverses and spline projectors. (English) Zbl 0519.41016 J. Approximation Theory 38, 269-278 (1983). Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page Cited in 2 ReviewsCited in 15 Documents 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 Keywords:generalized inverse; abstract spline; spline projector; Hilbert space; spline interpolant Citations:Zbl 0491.41016; Zbl 0477.41012 PDF BibTeX XML Cite \textit{S. Izumino}, J. Approx. Theory 38, 269--278 (1983; Zbl 0519.41016) Full Text: DOI OpenURL References: [1] Anselone, P.M; Nashed, M.Z, Perturbations of outer inverses, (), 163-168 · Zbl 0476.47007 [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. [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 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 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] () [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 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. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.