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.

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