Optimal solvers for linear systems with fractional powers of sparse SPD matrices Academic Article uri icon

abstract

  • Copyright © 2018 John Wiley & Sons, Ltd. In this paper, we consider efficient algorithms for solving the algebraic equation Aαu=f, 0<α<1, where A is a properly scaled symmetric and positive definite matrix obtained from finite difference or finite element approximations of second-order elliptic problems in ℝ, d=1,2,3. This solution is then written as u=Aβ-α with F=A-βf with β positive integer. The approximate solution method we propose and study is based on the best uniform rational approximation of the function tβ−α for 0

author list (cited authors)

  • Harizanov, S., Lazarov, R., Margenov, S., Marinov, P., & Vutov, Y.

citation count

  • 26

publication date

  • October 2018

publisher