In this paper we extend to the multidimensional case six free-derivative iterative methods that are known in their scalar version. In order to construct new multidimensional iterative algorithms we develop a new idea based on two operators. All the schemes considered here are two-step methods in which the first step is Steffensen’s method and they have fourth-order local convergence, depending on the function. We analyze the efficiency of these six new algorithms and conclude which ones are the most efficient. We illustrate these results with some numerical examples, where their order of convergence is discussed. Finally, a study comparing the efficiency and elapsed time of the suggested methods supports the claimed theoretical results.
SeMA Journal – Springer Journals
Published: Nov 18, 2016
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