4. Methods for uTf (A)v

In this section we describe how to use quadrature methods to calculate approximations of u ^T f (A)v (see ). The matrix A is assumed to be real symmetric and we use the spectral decomposition of A written as A = ZDZ ^T , where Z is an orthonormal matrix whose columns are the normalized eigenvectors of A and D is a diagonal matrix whose diagonal elements are the eigenvalues λ _i of A, which are ordered as follows...