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Splines and pseudo-inverses. (English) Zbl 0393.65022


MSC:

65J10 Numerical solutions to equations with linear operators
41A15 Spline approximation
47A05 General (adjoints, conjugates, products, inverses, domains, ranges, etc.)
46M05 Tensor products in functional analysis
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References:

[1] 1. J. M. BEREZANSKIJ, Expansions in Eigenfunctions of SelfadjointOperator, ,Amer Math. Soc, Providence, R. I., 1968. Zbl0157.16601 · Zbl 0157.16601
[2] 2. F. J. DELVOS and H. POSDORF, On Optimal Tensor Product Approximation, J. Approximation Theory, Vol. 18, 1976,pp.99-107. Zbl0442.41002 MR438012 · Zbl 0442.41002 · doi:10.1016/0021-9045(76)90098-8
[3] 3. F. J. DELVOS and K. H. SCHLOSSER, Das Tensorprodukt-Schema von Spline Systemen in Spline-Funktionen K. Böhmer, G. Meinardus, W. Schempp, Mannheim, Wien-Ziirich, Bibliographisches Institut, 1974. Zbl0295.41009 MR412679 · Zbl 0295.41009
[4] 4. C. A. DESOER and B. H. WHALEN, A note on Pseudo-inverses, J. Soc. Industr. Math,,Vol. 11, 1963, pp.442-447. Zbl0123.09603 MR156199 · Zbl 0123.09603 · doi:10.1137/0111031
[5] 5. T. N. E. GREVILLE, Note on Fitting Functions ofSeveral Variables, J. Soc. Industr.Appl. Math., Vol. 9, 1961, pp. 109-115. Zbl0168.14902 MR129112 · Zbl 0168.14902 · doi:10.1137/0109011
[6] 6. F. J. HALL, Generalized Inverses of a Bordered Matrix of Operators, S.I.A.M .J. Appl. Math., Vol. 29, 1975 , pp. 152-163. Zbl0324.47007 MR372643 · Zbl 0324.47007 · doi:10.1137/0129015
[7] 7. W. HAUSSMANN, On Multivariate Spline Systems, . Approximation Theory, Vol.11, 1974, pp.285-305. Zbl0292.41009 MR358153 · Zbl 0292.41009 · doi:10.1016/0021-9045(74)90001-X
[8] 8. W. HAUSSMANN and H. J. MÜNCH, On the Construction of Multivariate Spline Systems in Approximation Theory, G. G. Lorentz, New York, London, Academic Press, 1973, pp.337-378. Zbl0334.41005 MR333529 · Zbl 0334.41005
[9] 9. P. L. LAURENT, Approximation et optimisation, Paris, Hermann, 1972. Zbl0238.90058 MR467080 · Zbl 0238.90058
[10] 10. N. MINAMIDE and K. NAKAMURA, A Restricted Pseudo-Inverse and its Application to Constrained minima, S.I.A.M. J. Appl. Math., Vol. 19, 1970 ,pp 167-177. Zbl0299.15003 MR268692 · Zbl 0299.15003 · doi:10.1137/0119015
[11] 11. W. PETRYSHYN, On Generalized Inverses and on the Uniform Convergence of (I-ßK)n with Application to Itérative Methods, J. Math. Anal, and Appl., Vol.18, 1967 pp. 417-439. Zbl0189.47502 MR208381 · Zbl 0189.47502 · doi:10.1016/0022-247X(67)90036-4
[12] 12. A. SARD, Optimal Approximation, J. Funct. Anal., Vol. 1, 1967, pp. 222-244. Zbl0158.13601 MR219967 · Zbl 0158.13601 · doi:10.1016/0022-1236(67)90033-X
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