Overview of Krylov subspace methods with applications to control problems
作者： Youcef Saad
DOI:
关键词: Applied mathematics 、 Eigenvalues and eigenvectors 、 Mathematical optimization 、 Krylov subspace 、 Mathematics 、 Conjugate residual method 、 Iterative method 、 Projection (linear algebra) 、 Generalized minimal residual method 、 Linear subspace 、 Subspace topology
摘要: An overview of projection methods based on Krylov subspaces are given with emphasis their application to solving matrix equations that arise in control problems. The main idea subspace is generate a basis the Span and seek an approximate solution original problem from this subspace. Thus, size N approximated by one dimension m typically much smaller than N. have been very successful linear systems eigenvalue problems now just becoming popular for nonlinear equations. It shown how they can be used solve partial pole placement problems, Sylvester's equation, Lyapunov's equation.
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