Parallel stochastic estimation method of eigenvalue distribution. (English) Zbl 1271.65063

Futamura, Yasunori; Tadano, Hiroto; Sakurai, Tetsuya

JSIAM Lett. 2, 127-130 (2010).

Summary: Some kinds of eigensolvers for large sparse matrices require specification of parameters that are based on rough estimates of the desired eigenvalues. In this paper, we propose a stochastic estimation method of eigenvalue distribution using the combination of a stochastic estimator of the matrix trace and contour integrations. The proposed method can be easily parallelized and applied to matrices for which factorization is infeasible. Numerical experiments are executed to show that the method can perform rough estimates at a low computational cost.

MSC:

65F15	Numerical computation of eigenvalues and eigenvectors of matrices
65F50	Computational methods for sparse matrices
65Y05	Parallel numerical computation

Keywords:

contour integration; stochastic estimation; parallel computation; large sparse matrices; eigenvalues; numerical experiments

Software:

MatrixMarket; zPARES