TY - JOUR
T1 - Gauss–Laurent-type quadrature rules for the approximation of functionals of a nonsymmetric matrix
AU - Alahmadi, J.
AU - Alqahtani, H.
AU - Pranić, M. S.
AU - Reichel, L.
N1 - Publisher Copyright:
© 2021, The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature.
PY - 2021/12
Y1 - 2021/12
N2 - This paper is concerned with the approximation of matrix functionals of the form wTf(A)v, where A∈ ℝn×n is a large nonsymmetric matrix, w, v∈ ℝn, and f is a function such that f(A) is well defined. We derive Gauss–Laurent quadrature rules for the approximation of these functionals, and also develop associated anti-Gauss–Laurent quadrature rules that allow us to estimate the quadrature error of the Gauss–Laurent rule. Computed examples illustrate the performance of the quadrature rules described.
AB - This paper is concerned with the approximation of matrix functionals of the form wTf(A)v, where A∈ ℝn×n is a large nonsymmetric matrix, w, v∈ ℝn, and f is a function such that f(A) is well defined. We derive Gauss–Laurent quadrature rules for the approximation of these functionals, and also develop associated anti-Gauss–Laurent quadrature rules that allow us to estimate the quadrature error of the Gauss–Laurent rule. Computed examples illustrate the performance of the quadrature rules described.
KW - Anti-Gauss–Laurent quadrature
KW - Extended Krylov subspace
KW - Gauss–Laurent quadrature
KW - Matrix function evaluation
KW - Orthogonal Laurent polynomial
UR - http://www.scopus.com/inward/record.url?scp=85105507694&partnerID=8YFLogxK
U2 - 10.1007/s11075-021-01101-0
DO - 10.1007/s11075-021-01101-0
M3 - Article
AN - SCOPUS:85105507694
SN - 1017-1398
VL - 88
SP - 1937
EP - 1964
JO - Numerical Algorithms
JF - Numerical Algorithms
IS - 4
ER -