Luo, Z. and J. Levesley, Error estimates and convergence rates for variational Hermite interpolation, J. Approx. Theory 95 (1998), 264--279.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....are many known error estimates for this type of Lagrange interpolation in the literature, including [9,12,14,26] For our purposes, the approach taken in [14] will prove most useful. In addition, the work presented here also draws on some ideas from other recent sources on interpolation in IR m [18,23], solving differential equations in IR m using collocation [4,7,8] and spherical interpolation and approximation [5,10,17] The system of equations (2) can be interpreted as a generalized Hermite interpolation problem. Generalized Hermite interpolation on spheres and on other differentiable ....

Luo, Z. and J. Levesley, Error estimates and convergence rates for variational Hermite interpolation, J. Approx. Theory 95 (1998), 264--279.

....(L; fl h) L; fl) H = L h; fl h) h = L h; f fl ) h = L h; f) h ; which proves (b) As in [12] it is possible to describe more explicitly the elements of C h . However, here we are mainly concerned with producing an error estimate. To see how we do this in detail the reader is referred to [9], but here it is more appropriate to appeal to the general setting of Atteia to indicate how the required estimate is obtained. The important ingredients of the theory are the semi Hilbert space C h , the reproducing kernel property (Theorem 1 (b) and the set , which by Theorem 1 (a) is a set ....

Z. Luo and J. Levesley, Error estimates and convergence rates for variational Hermite interpolation, Research Report 1997/6, Department of Mathematics and Computer Science, University of Leicester, Leicester LE1 7RH, UK.

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