TY  - JOUR
AU  - Reichel, Lothar
AU  - Spalević, Miodrag
AU  - Tang, Tunan
PY  - 2016
UR  - https://machinery.mas.bg.ac.rs/handle/123456789/2489
AB  - The need to compute expressions of the form , where A is a large square matrix, u and v are vectors, and f is a function, arises in many applications, including network analysis, quantum chromodynamics, and the solution of linear discrete ill-posed problems. Commonly used approaches first reduce A to a small matrix by a few steps of the Hermitian or non-Hermitian Lanczos processes and then evaluate the reduced problem. This paper describes a new method to determine error estimates for computed quantities and shows how to achieve higher accuracy than available methods for essentially the same computational effort. Our methods are based on recently proposed generalized averaged Gauss quadrature formulas.
PB  - Springer, Dordrecht
T2  - Bit Numerical Mathematics
T1  - Generalized averaged Gauss quadrature rules for the approximation of matrix functionals
EP  - 1067
IS  - 3
SP  - 1045
VL  - 56
DO  - 10.1007/s10543-015-0592-7
ER  - 

@article{
author = "Reichel, Lothar and Spalević, Miodrag and Tang, Tunan",
year = "2016",
abstract = "The need to compute expressions of the form , where A is a large square matrix, u and v are vectors, and f is a function, arises in many applications, including network analysis, quantum chromodynamics, and the solution of linear discrete ill-posed problems. Commonly used approaches first reduce A to a small matrix by a few steps of the Hermitian or non-Hermitian Lanczos processes and then evaluate the reduced problem. This paper describes a new method to determine error estimates for computed quantities and shows how to achieve higher accuracy than available methods for essentially the same computational effort. Our methods are based on recently proposed generalized averaged Gauss quadrature formulas.",
publisher = "Springer, Dordrecht",
journal = "Bit Numerical Mathematics",
title = "Generalized averaged Gauss quadrature rules for the approximation of matrix functionals",
pages = "1067-1045",
number = "3",
volume = "56",
doi = "10.1007/s10543-015-0592-7"
}

Reichel, L., Spalević, M.,& Tang, T.. (2016). Generalized averaged Gauss quadrature rules for the approximation of matrix functionals. in Bit Numerical Mathematics
Springer, Dordrecht., 56(3), 1045-1067.
https://doi.org/10.1007/s10543-015-0592-7

Reichel L, Spalević M, Tang T. Generalized averaged Gauss quadrature rules for the approximation of matrix functionals. in Bit Numerical Mathematics. 2016;56(3):1045-1067.
doi:10.1007/s10543-015-0592-7 .

Reichel, Lothar, Spalević, Miodrag, Tang, Tunan, "Generalized averaged Gauss quadrature rules for the approximation of matrix functionals" in Bit Numerical Mathematics, 56, no. 3 (2016):1045-1067,
https://doi.org/10.1007/s10543-015-0592-7 . .