The analytic structure of Rational Interpolants (R.I.) f (z) built from randomly perturbed data is explored; the interpolation nodes x j , j = 1,...,M, are real points where the function f reaches these prescribed data $$\widetilde\phi _j$$ . It is assumed that the data $$\widetilde\phi _j$$ are randomly perturbed values of a rational function ϕ(n) (m) (m / n is the degree of the numerator/denominator). Much attention is paid to the R.I. familyf (n+1) (m−1), in the small stochasticity régime. The main result is that the additional zero and pole are located nearby the root of the same random polynomial, called the Froissart Polynomial (F.P.). With gaussian hypothesis on the noise, the random real root of F.P. is distributed according to a Cauchy-Lorentz law, with parameters such that the integrated probability over the interpolation interval ⌈x 1, x M ⌉ is always larger than 1/2; in two cases studied in detail, it reaches 2/3 in one case and almost 3/4 in the other. For the families f (n+k) (m+k), numerical explorations point to similar phenomena; inspection shows that, in the mean, the localization occurs in the complex and/or real vicinity of the interpolation interval.
Reliable Computing – Springer Journals
Published: Oct 16, 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.
Get unlimited, online access to over 18 million full-text articles from more than 15,000 scientific journals.
Read from thousands of the leading scholarly journals from SpringerNature, Elsevier, Wiley-Blackwell, Oxford University Press and more.
All the latest content is available, no embargo periods.
“Hi guys, I cannot tell you how much I love this resource. Incredible. I really believe you've hit the nail on the head with this site in regards to solving the research-purchase issue.”Daniel C.
“Whoa! It’s like Spotify but for academic articles.”@Phil_Robichaud
“I must say, @deepdyve is a fabulous solution to the independent researcher's problem of #access to #information.”@deepthiw
“My last article couldn't be possible without the platform @deepdyve that makes journal papers cheaper.”@JoseServera