Title :
A Grassmann-Rayleigh quotient iteration for computing invariant subspaces
Author :
Absil, P.-A. ; Mahony, Robert ; Sepulchre, R. ; Van Dooren, P.
Author_Institution :
Inst. Montefiore, Liege Univ., Belgium
Abstract :
The classical Rayleigh quotient iteration (RQI) computes a 1-dimensional invariant subspace of a symmetric matrix A with cubic convergence. We propose a generalization of the RQI which computes a p-dimensional invariant subspace of A. The geometry of the algorithm on the Grassmann manifold Gr(p,n) is developed to show cubic convergence and to draw connections with Newton algorithms on Riemannian manifolds
Keywords :
convergence; geometry; iterative methods; matrix algebra; 1-dimensional invariant subspace; Grassmann manifold; Grassmann-Rayleigh quotient iteration; Riemannian manifolds; cubic convergence; p-dimensional invariant subspace; symmetric matrix; Computational geometry; Convergence; Costs; Displays; Eigenvalues and eigenfunctions; Instruments; Mathematics; Matrix decomposition; Q factor; Riccati equations;
Conference_Titel :
Decision and Control, 2000. Proceedings of the 39th IEEE Conference on
Conference_Location :
Sydney, NSW
Print_ISBN :
0-7803-6638-7
DOI :
10.1109/CDC.2001.914565
