Error Inequalities in Polynomial Interpolation and Their Applications O.P And of his Opponent

And of his Opponent

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Error Inequalities in Polynomial Interpolation and Their Applications O.P And of his OpponentGiven 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