Error Inequalities in Polynomial Interpolation and Their Applications:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Dordrecht
Springer Netherlands
1993
|
| Schriftenreihe: | Mathematics and Its Applications
262 |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Beschreibung: | 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; (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 < C k(b -at- max I x{n)(t) I, 0< k < 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 |
| Beschreibung: | 1 Online-Ressource (X, 366 p) |
| ISBN: | 9789401120265 9789401048965 |
| DOI: | 10.1007/978-94-011-2026-5 |
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| 245 | 1 | 0 | |a Error Inequalities in Polynomial Interpolation and Their Applications |c by Ravi P. Agarwal, Patricia J. Y. Wong |
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Datensatz im Suchindex
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| isbn | 9789401120265 9789401048965 |
| language | English |
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| spelling | Agarwal, Ravi P. Verfasser aut Error Inequalities in Polynomial Interpolation and Their Applications by Ravi P. Agarwal, Patricia J. Y. Wong Dordrecht Springer Netherlands 1993 1 Online-Ressource (X, 366 p) txt rdacontent c rdamedia cr rdacarrier Mathematics and Its Applications 262 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; (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 < C k(b -at- max I x{n)(t) I, 0< k < 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 Mathematics Differential Equations Computer science / Mathematics Approximations and Expansions Computational Mathematics and Numerical Analysis Applications of Mathematics Ordinary Differential Equations Informatik Mathematik Fehlerabschätzung (DE-588)4228085-0 gnd rswk-swf Polynom-Interpolationsverfahren (DE-588)4175264-8 gnd rswk-swf Polynom-Interpolationsverfahren (DE-588)4175264-8 s Fehlerabschätzung (DE-588)4228085-0 s 1\p DE-604 Wong, Patricia J. Y. Sonstige oth https://doi.org/10.1007/978-94-011-2026-5 Verlag Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Agarwal, Ravi P. Error Inequalities in Polynomial Interpolation and Their Applications Mathematics Differential Equations Computer science / Mathematics Approximations and Expansions Computational Mathematics and Numerical Analysis Applications of Mathematics Ordinary Differential Equations Informatik Mathematik Fehlerabschätzung (DE-588)4228085-0 gnd Polynom-Interpolationsverfahren (DE-588)4175264-8 gnd |
| subject_GND | (DE-588)4228085-0 (DE-588)4175264-8 |
| title | Error Inequalities in Polynomial Interpolation and Their Applications |
| title_auth | Error Inequalities in Polynomial Interpolation and Their Applications |
| title_exact_search | Error Inequalities in Polynomial Interpolation and Their Applications |
| title_full | Error Inequalities in Polynomial Interpolation and Their Applications by Ravi P. Agarwal, Patricia J. Y. Wong |
| title_fullStr | Error Inequalities in Polynomial Interpolation and Their Applications by Ravi P. Agarwal, Patricia J. Y. Wong |
| title_full_unstemmed | Error Inequalities in Polynomial Interpolation and Their Applications by Ravi P. Agarwal, Patricia J. Y. Wong |
| title_short | Error Inequalities in Polynomial Interpolation and Their Applications |
| title_sort | error inequalities in polynomial interpolation and their applications |
| topic | Mathematics Differential Equations Computer science / Mathematics Approximations and Expansions Computational Mathematics and Numerical Analysis Applications of Mathematics Ordinary Differential Equations Informatik Mathematik Fehlerabschätzung (DE-588)4228085-0 gnd Polynom-Interpolationsverfahren (DE-588)4175264-8 gnd |
| topic_facet | Mathematics Differential Equations Computer science / Mathematics Approximations and Expansions Computational Mathematics and Numerical Analysis Applications of Mathematics Ordinary Differential Equations Informatik Mathematik Fehlerabschätzung Polynom-Interpolationsverfahren |
| url | https://doi.org/10.1007/978-94-011-2026-5 |
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