Abstract
We study the existence, uniqueness and approximation properties of rational complex planar spline interpolants of order (3, 1). We also find sufficient conditions for such interpolants to be quasiregular and quasiconformal. Examples are given.
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J.H. Ahlberg, E.N. Nilson and J.L. Walsh, Complex cubic splines, Trans. Amer. Math. Soc. 129(1967)391–413.
L.V. Ahlfors,Lectures on Quasiconformal Mappings, Van Nostrand Mathematical Studies, Vol. 10 (1966).
I. Babuska, B. Szabo and I. Katz, The ρ-version of the finite element method, SIAM J. Numer. Anal. 18(1981)515–545.
H.P. Dikshit and A. Ojha, On convergence and quasiconformality of complex planar spline interpolants, Math. Proc. Camb. Phil. Soc. 99(1986)347–356.
H.P. Dikshit, A. Ohja and A. Sharma, Certain mapping properties of rational complex planar splines, Math. Proc. Camb. Phil Soc. 101(1987)141–149.
G. Martio, S. Rickman and J. Väisälä, Definitions for quasiregular mappings, Ann. Acad. Sci. Fenn. Ser. AI, Vol. 449(1969).
G. Opfer and M.L. Puri, Complex planar splines, J. Approx. Theory 31(1981)383–402.
G. Opfer and G. Schober, On convergence and quasiregularity of interpolating complex planar splines, Math. Z. 180(1982)469–481.
E.L. Wachspress,A Rational Finite Element Basis (Academic Press, 1975).
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This work was carried out with the aid of MACSYMA, a large symbolic manipulation program developed at the MIT Laboratory for Computer Science and supported from 1975 to 1983 by the National Aeronautics and Space Administration under grant NSG 1323, by the Office of Naval Research under grant N00014-77C-0641, by the U.S. Department of Energy under grant ET-78-C-024687, and by the U.S. Air Force under grant F49620-79-C-020, and since 1982 by Symbolics, Inc. of Burlington, MA.
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Dikshit, H.P., Ojha, A. & Zalik, R.A. Wachspress type rational complex planar splines of degree (3,1). Adv Comput Math 2, 235–249 (1994). https://doi.org/10.1007/BF02521110
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DOI: https://doi.org/10.1007/BF02521110