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Article | REF: AF486 V1

Matrix Functions Computations

Author: Gérard MEURANT

Publication date: October 10, 2014, Review date: April 26, 2021

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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

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