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An extension of Gander’s result for quadratic equations

✍ Scribed by J.A. Ezquerro; M.A. Hernández; N. Romero

Publisher
Elsevier Science
Year
2010
Tongue
English
Weight
393 KB
Volume
234
Category
Article
ISSN
0377-0427

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✦ Synopsis

In the study of iterative methods with high order of convergence, Gander provides a general expression for iterative methods with order of convergence at least three in the scalar case. Taking into account an extension of this result, we define a family of iterations in Banach spaces with R-order of convergence at least four for quadratic equations.

📜 SIMILAR VOLUMES

An extension result for continuous valua
An extension result for continuous valuations
✍ M. Alvarez-Manilla; A. Edalat; N. Saheb-Djahromi 📂 Article 📅 1998 🏛 Elsevier Science 🌐 English ⚖ 773 KB

We show, by a simple and direct proof, that if a bounded valuation on a directed complete partial order (dcpo) is the supremum of a directed family of simple valuations then it has a unique extension to a measure on the Borel -algebra of the dcpo with the Scott topology. It follows that every bounde