The basic problem of interval computations is: given a function f(x 1,..., x n) and n intervals [x i, x i], find the (interval) range yof the given function on the given intervals. It is known that even for quadratic polynomials f(x 1,..., x n), this problem is NP-hard. In this paper, following the advice of A. Neumaier, we analyze the complexity of asymptotic range estimation, when the bound ε on the width of the input intervals tends to 0. We show that for small c > 0, if we want to compute the range with an accuracy c ⋅ ε2, then the problem is still NP-hard; on the other hand, for every δ > 0, there exists a feasible algorithm which asymptotically, estimates the range with an accuracy c ⋅ ε2−δ.
Reliable Computing – Springer Journals
Published: Oct 13, 2004
It’s your single place to instantly
discover and read the research
that matters to you.
Enjoy affordable access to
over 18 million articles from more than
15,000 peer-reviewed journals.
All for just $49/month
Query the DeepDyve database, plus search all of PubMed and Google Scholar seamlessly
Save any article or search result from DeepDyve, PubMed, and Google Scholar... all in one place.
All the latest content is available, no embargo periods.
“Whoa! It’s like Spotify but for academic articles.”@Phil_Robichaud