Newton’s method for concave operators with resolvent positive derivatives in ordered Banach spaces

We prove a non-local convergence result for Newton’s method applied to a class of nonlinear equations in ordered real Banach spaces. The key tools in our approach are special notions of concavity and the spectral theory of resolvent positive operators.

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Vydané v:	Linear algebra and its applications Ročník 363; s. 43 - 64
Hlavní autori:	Damm, T., Hinrichsen, D.
Médium:	Journal Article Konferenčný príspevok..
Jazyk:	English
Vydavateľské údaje:	New York, NY Elsevier Inc 01.04.2003 Elsevier Science
Predmet:	Algebra Concave operators Exact sciences and technology Linear and multilinear algebra, matrix theory Mathematics Newton’s method Positive operators Riccati equation Sciences and techniques of general use Concave operators 15A24 Newton’s method 47H07 47J25 Riccati equation 65J15 Positive operators
ISSN:	0024-3795, 1873-1856
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Popis
Shrnutí:	We prove a non-local convergence result for Newton’s method applied to a class of nonlinear equations in ordered real Banach spaces. The key tools in our approach are special notions of concavity and the spectral theory of resolvent positive operators.
ISSN:	0024-3795 1873-1856
DOI:	10.1016/S0024-3795(02)00328-2