The modified Newton–Shamanskii method for the solution of a quadratic vector equation arising in Markovian binary trees

Autor:	Pei-Chang Guo, Shu-Fang Xu
Rok vydání:	2014
Předmět:	Sequence Algebra and Number Theory Binary tree Numerical analysis Mathematical analysis Markov process Monotonic function System of linear equations Computational Mathematics symbols.namesake Quadratic equation Theory of computation symbols Mathematics
Zdroj:	Calcolo. 52:317-325
ISSN:	1126-5434 0008-0624
DOI:	10.1007/s10092-014-0118-8
Popis:	In order to determine the extinction probability of a Markovian binary tree, it is necessary to find the minimal nonnegative solution of a quadratic vector equation. We apply the modified Newton---Shamanskii method for solving the equation. We show that the sequence of vectors generated by the modified Newton---Shamanskii method is monotonically increasing and converges to the minimal nonnegative solution of the equation. Numerical experiments show the effectiveness of our method.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_________::d2f6773b36fee093dc8c583e9efeb940 https://doi.org/10.1007/s10092-014-0118-8 Zobrazit plný text záznamu Full text from SpringerLink