Error Inequalities in Polynomial Interpolation and Their Applications PDF
R. P. AgarwalGiven a function x(t) E c{n) [a, bj, points a = al < a2 < . . . < ar = b and subsets aj of {0,1,,n -1} with L:j=lcard(aj) = n, the classical interpolation problem is to find a polynomial P - (t) of degree at most (n - 1) n l such that P~~l(aj) = x{i)(aj) for i E aj, j = 1,2, r. In the first four chapters of this monograph we shall consider respectively the cases: the Lidstone interpolation (a = 0, b = 1, n = 2m, r = 2, al = a2 = {a, 2, 2m - 2}), the Hermite interpolation (aj = {a, 1, , kj - I}), the Abel - Gontscharoff interpolation (r = n, ai ~ ai+l, aj = {j - I}), and the several particular cases of the Birkhoff interpolation. For each of these problems we shall offer: (1) explicit representations of the interpolating polynomial
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Generalization of weighted Ostrowski type inequalities by ...
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APPROXIMATION THEORY VIII-Vol. 1 APPROXIMATION AND ... APPROXIMATION THEORY VIII-Vol. 1 APPROXIMATION AND INTERPOLATION College Station, Texas, USA 8-12 January 1995 edited by C. K. Chui Center for Approximation Theory Texas A&M University L L. Schumaker Department of Mathematics Vanderbilt University Vfe World Scientific «• Singapore • New Jersey London • Hong Kong
21 May 2018 ... Most of error analysis of polynomial interpolation employs L∞ norm. ... The bound n!hn+14 is not very small compared that in Chebyshev nodes. ... book " Error Inequalities in Polynomial Interpolation and Their Applications" by ...
In our earlier work [1, 2] we have shown that the interpolating polynomial theory and the qualitative as well as quantitative study of boundary value problems such as existence and uniqueness of solutions, and convergence of various iterative methods are directly connected.In this paper we will extend this technique to the following complementary Lidstone boundary value problem …