Optimal solvers for linear systems with fractional powers of sparse SPD matrices
Stanislav Harizanov, Raytcho Lazarov, S. Margenov, P. Marinov, Yavor Vutov · Numerical Linear Algebra with Applications · 2018
Summary In this paper, we consider efficient algorithms for solving the algebraic equation , 0<α<1, where is a properly scaled symmetric and positive definite matrix obtained from finite difference or finite element approximations of second‐order elliptic problems in , d=1,2,3. This solution is then written as with 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