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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Vydáno v:Linear algebra and its applications Ročník 363; s. 43 - 64
Hlavní autoři: Damm, T., Hinrichsen, D.
Médium: Journal Article Konferenční příspěvek
Jazyk:angličtina
Vydáno: New York, NY Elsevier Inc 01.04.2003
Elsevier Science
Témata:
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