Szczegóły publikacji
Opis bibliograficzny
On the optimal robust solution of IVPs with noisy information / Bolesław KACEWICZ, Paweł PRZYBYŁOWICZ // Numerical Algorithms ; ISSN 1017-1398. — 2016 — vol. 71 iss. 3, s. 505–518. — Bibliogr. s. 517–518, Abstr. — Publikacja dostępna online od: 2015-06-07
Autorzy (2)
Słowa kluczowe
Dane bibliometryczne
| ID BaDAP | 96513 |
|---|---|
| Data dodania do BaDAP | 2016-03-09 |
| Tekst źródłowy | URL |
| DOI | 10.1007/s11075-015-0006-6 |
| Rok publikacji | 2016 |
| Typ publikacji | artykuł w czasopiśmie |
| Otwarty dostęp |  |
| Czasopismo/seria | Numerical Algorithms |
Abstract
We investigate the optimal solution of systems of initial-value problems with smooth right-hand side functions f from a Holder class ¨ Fr, reg , where r ≥ 0 is the number of continuous derivatives of f , and ∈ (0, 1] is the Holder exponent of ¨ rth partial derivatives. We consider algorithms that use n evaluations of f , the ith evaluation being corrupted by a noise δi of deterministic or random nature. For δ ≥ 0, in the deterministic case the noise δi is a bounded vector, δi ≤ δ. In the random case, it is a vector-valued random variable bounded in average, (E(δiq )) 1/q ≤ δ, q ∈ [1, +∞). We point out an algorithm whose Lp error (p ∈ [0, +∞]) is O(n−(r+) + δ), independently of the noise distribution. We observe that the level n−(r+) +δ cannot be improved in a class of information evaluations and algorithms. For ε 0, and a certain model of δ-dependent cost, we establish optimal values of n(ε) and δ(ε) that should be used in order to get the error at most ε with minimal cost.