Studies on Jacobi–Davidson, Rayleigh quotient iteration, inverse iteration generalized Davidson and Newton updates

2006 ◽  
Vol 13 (8) ◽  
pp. 621-642 ◽  
Author(s):  
Yunkai Zhou
Keyword(s):  
Rayleigh Quotient ◽  
Inverse Iteration ◽  
Rayleigh Quotient Iteration

scholarly journals Rank-1 perturbations and the Lanczos method, inverse iteration, and Krylov subspaces

1995 ◽  
Vol 36 (4) ◽  
pp. 381-388 ◽  
Author(s):  
Christopher T. Lenard
Keyword(s):  
Global Convergence ◽  
Krylov Subspace ◽  
Invariant Subspaces ◽  
Rayleigh Quotient ◽  
Lanczos Method ◽  
Krylov Subspaces ◽  
Inverse Iteration ◽  
Lanczos Algorithm ◽  
Orthonormal Bases ◽  
Rayleigh Quotient Iteration

AbstractThe heart of the Lanczos algorithm is the systematic generation of orthonormal bases of invariant subspaces of a perturbed matrix. The perturbations involved are special since they are always rank-1 and are the smallest possible in certain senses. These minimal perturbation properties are extended here to more general cases.Rank-1 perturbations are also shown to be closely connected to inverse iteration, and thus provide a novel explanation of the global convergence phenomenon of Rayleigh quotient iteration.Finally, we show that the restriction to a Krylov subspace of a matrix differs from the restriction of its inverse by a rank-1 matrix.

Quantum algorithm for Laplacian eigenmap via Rayleigh quotient iteration

2021 ◽  
Vol 21 (1) ◽  
Author(s):  
Ze-Tong Li ◽  
Fan-Xu Meng ◽  
Xu-Tao Yu ◽  
Zai-Chen Zhang
Keyword(s):  
Quantum Algorithm ◽  
Rayleigh Quotient ◽  
Rayleigh Quotient Iteration

scholarly journals Multigrid Discretization and Iterative Algorithm for Mixed Variational Formulation of the Eigenvalue Problem of Electric Field

2012 ◽  
Vol 2012 ◽  
pp. 1-25 ◽  
Author(s):  
Yidu Yang ◽  
Yu Zhang ◽  
Hai Bi
Keyword(s):  
Finite Element ◽  
Eigenvalue Problem ◽  
Electric Field ◽  
Adaptive Algorithm ◽  
Variational Formulation ◽  
High Efficiency ◽  
Mixed Finite Element ◽  
Mixed Finite Element Method ◽  
Rayleigh Quotient ◽  
Rayleigh Quotient Iteration

This paper discusses highly finite element algorithms for the eigenvalue problem of electric field. Combining the mixed finite element method with the Rayleigh quotient iteration method, a new multi-grid discretization scheme and an adaptive algorithm are proposed and applied to the eigenvalue problem of electric field. Theoretical analysis and numerical results show that the computational schemes established in the paper have high efficiency.

Sign in / Sign up

Export Citation Format

Share Document