TY  - JOUR
AU  - Eshghi, Nasim
AU  - Reichel, Lothar
AU  - Spalević, Miodrag
PY  - 2017
UR  - https://machinery.mas.bg.ac.rs/handle/123456789/2731
AB  - Matrix functions of the form f (A) v, where A is a large symmetric matrix, f is a function, and v not equal 0 is a vector, are commonly approximated by first applying a few, say n, steps of the symmetric Lanczos process to A with the initial vector v in order to determine an orthogonal section of A. The latter is represented by a (small) n x n tridiagonal matrix to which f is applied. This approach uses the n first Lanczos vectors provided by the Lanczos process. However, n steps of the Lanczos process yield n + 1 Lanczos vectors. This paper discusses how the (n + 1) st Lanczos vector can be used to improve the quality of the computed approximation of f (A) v. Also the approximation of expressions of the form v(T) f (A) v is considered.
PB  - Kent State University
T2  - Electronic Transactions on Numerical Analysis
T1  - Enhanced matrix function approximation
EP  - 205
SP  - 197
VL  - 47
UR  - https://hdl.handle.net/21.15107/rcub_machinery_2731
ER  - 

@article{
author = "Eshghi, Nasim and Reichel, Lothar and Spalević, Miodrag",
year = "2017",
abstract = "Matrix functions of the form f (A) v, where A is a large symmetric matrix, f is a function, and v not equal 0 is a vector, are commonly approximated by first applying a few, say n, steps of the symmetric Lanczos process to A with the initial vector v in order to determine an orthogonal section of A. The latter is represented by a (small) n x n tridiagonal matrix to which f is applied. This approach uses the n first Lanczos vectors provided by the Lanczos process. However, n steps of the Lanczos process yield n + 1 Lanczos vectors. This paper discusses how the (n + 1) st Lanczos vector can be used to improve the quality of the computed approximation of f (A) v. Also the approximation of expressions of the form v(T) f (A) v is considered.",
publisher = "Kent State University",
journal = "Electronic Transactions on Numerical Analysis",
title = "Enhanced matrix function approximation",
pages = "205-197",
volume = "47",
url = "https://hdl.handle.net/21.15107/rcub_machinery_2731"
}

Eshghi, N., Reichel, L.,& Spalević, M.. (2017). Enhanced matrix function approximation. in Electronic Transactions on Numerical Analysis
Kent State University., 47, 197-205.
https://hdl.handle.net/21.15107/rcub_machinery_2731

Eshghi N, Reichel L, Spalević M. Enhanced matrix function approximation. in Electronic Transactions on Numerical Analysis. 2017;47:197-205.
https://hdl.handle.net/21.15107/rcub_machinery_2731 .

Eshghi, Nasim, Reichel, Lothar, Spalević, Miodrag, "Enhanced matrix function approximation" in Electronic Transactions on Numerical Analysis, 47 (2017):197-205,
https://hdl.handle.net/21.15107/rcub_machinery_2731 .