Error Inequalities in Polynomial Interpolation and Their Applications.pdf

Error Inequalities in Polynomial Interpolation and Their Applications PDF

R. P. Agarwal

Given 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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3.76 MB DATEIGRÖSSE
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Error Inequalities in Polynomial Interpolation and Their Applications.pdf

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