Generalized averaged Gauss quadrature rules for the approximation of matrix functionals
Само за регистроване кориснике
2016
Чланак у часопису (Објављена верзија)
Метаподаци
Приказ свих података о документуАпстракт
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.
Кључне речи:
Matrix functional / Gauss quadrature / Averaged Gauss rulesИзвор:
Bit Numerical Mathematics, 2016, 56, 3, 1045-1067Издавач:
- Springer, Dordrecht
Финансирање / пројекти:
- Методе нумеричке и нелинеарне анализе са применама (RS-MESTD-Basic Research (BR or ON)-174002)
- NSF [DMS-1115385]
DOI: 10.1007/s10543-015-0592-7
ISSN: 0006-3835
WoS: 000382137200012
Scopus: 2-s2.0-84949763422
Колекције
Институција/група
Mašinski fakultetTY - 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 . .