Computing the matrix fractional power with the double exponential formula

Two quadrature-based algorithms for computing the matrix fractional power $A^\alpha$ are presented in this paper. These based on double exponential (DE) formula, which is well-known its effectiveness improper integrals as well treating nearly arbitrary endpoint singularities. The DE formula transforms a given integral into another that suited trapezoidal rule; process, interval transformed an infinite interval. Therefore, it necessary to truncate appropriate finite In paper, truncation method, error analysis specialized computation of $A^\alpha$, proposed. Then, two presented---one where computed with fixed number abscissa points and one adaptively. Subsequently, convergence rate Hermitian positive definite matrices analyzed. shows converges faster than Gaussian quadrature when $A$ ill-conditioned $\alpha$ non-unit fraction. Numerical results show our achieve required accuracy other several situations.