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Interpolation operators with applications. II. (English) Zbl 1172.41001

In this research exposition, some practical applications of blending interpolation are studied. Lagrange, Hermite and Birkhoff operators that interpolate a given function \(f\) and certain of its derivatives, defined on a given domain \(\Omega \subset\mathbb R^2\) are used. The authors first present a surface fitting technique under certain conditions of interpolation. This is followed by construction of roof-surfaces for large halls. Interpolatory type quadrature formulas have also been given [cf. L. F. Meyers and A. Sard, J. Math. Physics 29, 118–123 (1950; Zbl 0039.34201)]. Inverse interpolation method for approximate solution of non-linear equations has been discussed. Several examples have been given. The paper ends with a fairly complete list of 250 references.
[Part I, the authors, Sci. Math. Jpn. 68, No. 3, 383–416 (2008; Zbl 1171.41002).]

MSC:

41-02 Research exposition (monographs, survey articles) pertaining to approximations and expansions
41A05 Interpolation in approximation theory
41A15 Spline approximation
65-02 Research exposition (monographs, survey articles) pertaining to numerical analysis
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