Estimating the diagonal of matrix functions

The evaluation of the diagonal of matrix functions arises in many applications and an efficient approximation of it, without estimating the whole matrix f ( A ), would be useful. In the present paper, we compare and analyze the performance of three numerical methods adjusted to attain the estimation of the diagonal of matrix functions f ( A ), where A ∈ R p × pis a symmetric matrix and f a suitable function. The applied numerical methods are based on extrapolation and Gaussian quadrature rules. Various numerical results illustrating the effectiveness of these methods and insightful remarks about their complexity and accuracy are demonstrated. Copyright © 2016 John Wiley & Sons, Ltd.