Premium
Estimating the diagonal of matrix functions
Author(s) -
Fika Paraskevi,
Mitrouli Marilena,
Roupa Paraskevi
Publication year - 2018
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.4228
Subject(s) - mathematics , diagonal , extrapolation , diagonal matrix , gaussian quadrature , matrix (chemical analysis) , gaussian elimination , numerical analysis , function (biology) , gaussian , matrix function , algorithm , mathematical optimization , symmetric matrix , mathematical analysis , nyström method , integral equation , geometry , eigenvalues and eigenvectors , materials science , physics , quantum mechanics , evolutionary biology , biology , composite material
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.