{"product_id":"9789401048965","title":"Error Inequalities in Polynomial Interpolation and Their Applications (Mathematics and Its Applications) (Reprint)","description":"\u003cp\u003eGiven a function x(t) E c{n) [a, bj, points a = al \u0026lt; a2 \u0026lt; ...\u0026lt; 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; (2) explicit representations of the associated error function e(t) = x(t) - Pn-l(t); and (3) explicit optimal\/sharp constants Cn,k so that the inequalities k I e{k)(t) I \u0026lt; C k(b -at- max I x{n)(t) I, 0 n - 1 n -, a$t$b - are satisfied. In addition, for the Hermite interpolation we shall provide explicit opti- mal\/sharp constants C(n,p, v) so that the inequality II e(t) lip:::; C(n,p, v) II x{n)(t) 1111, p, v ~ 1 holds.\u003c\/p\u003e","brand":"Springer Verlag","offers":[{"title":"Default Title","offer_id":42574976581707,"sku":"00000_00000_00000_00000","price":1960.57,"currency_code":"THB","in_stock":true}],"url":"https:\/\/kinokuniya.co.th\/th\/products\/9789401048965","provider":"Books Kinokuniya Thailand","version":"1.0","type":"link"}