Presentation Information
[A-2-06]A combination of two iterative algorithms for solving real symmetric positive definite eigenvalue problems
◎Tetsuya Koga1, Takafumi Miyata1 (1. Fukuoka Institute of Technology)
Keywords:
Eigenvalue problem,Fast algorithm
Suppose we want to compute the smallest eigenvalue and its corresponding eigenvector of a real symmetric positive definite matrix.This problem arises in applications such as structural analysis.An approximate eigenvalue computed by EPIC (Eigensolver based on Preconditioning and Implicit Convexity) monotonically converges to the smallest eigenvalue.Although EPIC has this superior property, it requires many iterations when we need to compute both the eigenvalue and the eigenvector.This study presents a combination of EPIC and Rayleigh quotient iteration to compute the eigenvalue and the eigenvector faster.Specifically, we utilize EPIC having the monotonical convergence to predict the eigenvalue, and then we use Rayleigh quotient iteration to correct the predicted eigenvalue and compute the eigenvector.Numerical results show that this algorithm computes the eigenvalue and the eigenvector faster than EPIC.