Newton's method for concave operators with resolvent positive derivatives in ordered Banach spaces
type: Item
instance of: scholarly article
title: Newton's method for concave operators with resolvent positive derivatives in ordered Banach spaces
zbMATH Open document ID: 1019.65035
DOI: 10.1016/S0024-3795(02)00328-2
author: Tobias Damm
author: D. Hinrichsen
published in: Linear Algebra and its Applications
publication date: 2003-05-04T00:00:00Z
review text: The authors prove a non-local convergence result for Newton's method applied to a class of concave operator equations with resolvent positive derivatives in ordered Banach spaces. The key tools in their approach are special notions of concavity and the spectral theory of resolvent positive operators. Finally, the results are illustrated by applications to a number of rational matrix equations arising in various control and realization problems.
reviewed by: Yu Wenhuan
Mathematics Subject Classification ID: 65J15
Mathematics Subject Classification ID: 47J25
Mathematics Subject Classification ID: 65F30
Mathematics Subject Classification ID: 15A24
Mathematics Subject Classification ID: 47H07
zbMATH DE Number: 1903557
zbMATH Keywords: Newton's method
zbMATH Keywords: concave operator equations
zbMATH Keywords: ordered Banach spaces
zbMATH Keywords: Riccati equation
zbMATH Keywords: numerical examples
zbMATH Keywords: resolvent positive operators
zbMATH Keywords: rational matrix equations
describes a project that uses: Algorithm 432
MaRDI profile type: Publication
cites work: Resolvent Positive Operators
cites work: Algorithm 432 [C2]: Solution of the matrix equation AX + XB = C [F4]
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description: scientific article; zbMATH DE number 1903557