ZOLOTAREV QUADRATURE RULES AND LOAD BALANCING FOR THE FEAST EIGENSOLVER

Stefan Guettel (1) , Eric Polizzi (2) , Ping Tak Peter Tang (3) , Gautier Viaud (4)

1 University of Manchester [Manchester]
2 ECE - Department of Electrical and Computer Engineering - University of Massachusetts
3 Intel Corporation [Santa Clara]
4 MICS - Mathématiques et Informatique pour la Complexité et les Systèmes

The FEAST method for solving large sparse eigenproblems is equivalent to subspace iteration with an approximate spectral projector and implicit orthogonalization. This relation allows us to characterize the convergence of this method in terms of the error of a certain rational approximant to an indicator function. We propose improved rational approximants leading to FEAST variants with faster convergence, in particular, when using rational approximants based on the work of Zolotarev. Numerical experiments demonstrate the possible computational savings especially for pencils whose eigenvalues are not well separated and when the dimension of the search space is only slightly larger than the number of wanted eigenvalues. The new approach improves both convergence robustness and load balancing when FEAST runs on multiple search intervals in parallel.

Keywords: generalized eigenproblem; FEAST; quadrature; Zolotarev; filter design; load balancing

Domains: Mathematics [math]

Stefan Guettel, Eric Polizzi, Ping Tak Peter Tang, Gautier Viaud. ZOLOTAREV QUADRATURE RULES AND LOAD BALANCING FOR THE FEAST EIGENSOLVER. SIAM Journal on Scientific Computing, 2015, 37 (4), pp.A2100-A2122. ⟨10.1137/140980090⟩. ⟨hal-02418265⟩