A State Feedback Controller Used to Solve an Ill-posed Linear System by a GL(n, R) Iterative Algorithm
| Autor: | Chein-Shan Liu |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2013 |
| Předmět: |
Discrete mathematics
Residual dynamics Iterative method lcsh:T57-57.97 Linear system Invariant manifold State vector General Medicine Manifold Ill-posed linear system Lie-group GL(n Algebraic equation Quadratic equation Linear inverse problems lcsh:Applied mathematics. Quantitative methods Future cone Differential algebraic equation Mathematics |
| Zdroj: | Communications in Numerical Analysis, Vol 2013, Pp 1-22 (2013) |
| ISSN: | 2193-4215 |
| Popis: | Starting from a quadratic invariant manifold in terms of the residual vector ${\textbf r}={\textbf B}{\textbf x}-{\textbf b}$ for an $n$-dimensional ill-posed linear algebraic equations system ${\textbf B}{\textbf x}={\textbf b}$, we derive an ODEs system for ${\textbf x}$ which is equipped with a state feedback controller to enforce the orbit of the state vector ${\textbf x}$ on a specified manifold, whose residual-norm is exponentially decayed. To realize the above idea we develop a very powerful implicit scheme based on the novel $GL(n,{\mathbb R})$ Lie-group method to integrate the resultant differential algebraic equation (DAE). Through numerical tests of inverse problems we find that the present Lie-group DAE algorithm can significantly accelerate the convergence speed, and is robust enough against the random noise. |
| Databáze: | OpenAIRE |
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