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

DOI10.1016/S0024-3795(02)00328-2zbMath1019.65035MaRDI QIDQ1870040

Tobias Damm, Diederich Hinrichsen

Publication date: 4 May 2003

Published in: Linear Algebra and its Applications (Search for Journal in Brave)

zbMATH Keywords

Newton's methodnumerical examplesRiccati equationordered Banach spacesrational matrix equationsresolvent positive operatorsconcave operator equations

Mathematics Subject Classification ID

Iterative procedures involving nonlinear operators (47J25) Matrix equations and identities (15A24) Numerical solutions to equations with nonlinear operators (65J15) Monotone and positive operators on ordered Banach spaces or other ordered topological vector spaces (47H07)

Related Items

Stability of discrete-time positive evolution operators on ordered Banach spaces and applications, A numerical procedure to compute the stabilising solution of game theoretic Riccati equations of stochastic control, Differential equations with positive evolutions and some applications, Filtering \(\mathcal{S}\)-coupled algebraic Riccati equations for discrete-time Markov jump systems, Generalized coupled algebraic Riccati equations for discrete-time Markov jump with multiplicative noise systems, Stabilizing composite control for a class of linear systems modeled by singularly perturbed Itô differential equations, Computation of the stabilizing solution of game theoretic Riccati equation arising in stochastic \(H_\infty\) control problems, \(M\)-operators on partially ordered Banach spaces, On a class of rational matrix differential equations arising in stochastic control., Comparison theorems using general cones for norms of iteration matrices, A new class of nonsymmetric algebraic Riccati equations, Exact detectability and exact observability of discrete-time linear stochastic systems with periodic coefficients, Exact detectability: application to generalized Lyapunov and Riccati equations, State-feedback \(H^{\infty}\)-type control of linear systems with time-varying parameter uncertainty

Uses Software

• Algorithm 432

Cites Work

• Monotonicity of spectral radius for positive operators on ordered Banach spaces
• Stability radii of Metzler operators
• Positive operators and an inertia theorem
• Monotonie und Randspektrum bei vollstetigen Operatoren
• Nonsymmetric Algebraic Riccati Equations and Wiener--Hopf Factorization for M-Matrices
• Recursive Algorithms for Solving a Class of Nonlinear Matrix Equations with Applications to Certain Sensitivity Optimization Problems
• Analysis and modificaton of Newton’s method for algebraic Riccati equations
• Matrix quadratic equations
• Resolvent Positive Operators
• Algorithm 432 [C2: Solution of the matrix equation AX + XB = C [F4]]
• Newton’s Method for Convex Operators in Partially Ordered Spaces
• On a Matrix Riccati Equation of Stochastic Control
• Frobenius Theory of Positive Operators: Comparison Theorems and Applications
• Newton's method for a rational matrix equation occurring in stochastic control
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item