Name
Abstract | ||
|---|---|---|
Abstract Solutions φ(x) of the functional equation φ(φ(x)) = f (x) are called iterative roots of the given function f (x). They are of interest in dynamical systems, chaos and complexity theory and also in the modeling of certain industrial and financial processes. The problem of computing this “square root” of a function or operator remains a hard task. While the theory of functional equations provides some insight for real and complex valued functions, iterative roots of nonlinear mappings from \({\mathbb{R}^n}\) to \({\mathbb{R}^n}\) are less studied from a theoretical and computational point of view. Here we prove existence of iterative roots of a certain class of monotone mappings in \({\mathbb{R}^n}\) spaces and demonstrate how a method based on neural networks can find solutions to some examples that arise from simple physical dynamical systems. |
Year | DOI | Venue |
|---|---|---|
2013 | 10.1007/s11590-012-0532-2 | Optimization Letters |
Keywords | Field | DocType |
Iterative root,Monotone operator,Functional equation,Dynamical system | Discrete mathematics,Monotonic function,Mathematical optimization,Nonlinear system,Mathematical analysis,Dynamical systems theory,Operator (computer programming),Square root,Functional equation,Dynamical system,Mathematics,Monotone polygon | Journal |
Volume | Issue | ISSN |
7 | 8 | 1862-4480 |
Citations | PageRank | References |
0 | 0.34 | 1 |
Authors | ||
3 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Pando G. Georgiev | 1 | 31 | 3.18 |
| Lars Kindermann | 2 | 18 | 3.53 |
| Panos M. Pardalos | 3 | 3720 | 397.84 |