Enhanced matrix function approximation
Апстракт
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.
Кључне речи:
symmetric Lanczos process / matrix function / Gauss quadratureИзвор:
Electronic Transactions on Numerical Analysis, 2017, 47, 197-205Издавач:
- Kent State University
Финансирање / пројекти:
- Методе нумеричке и нелинеарне анализе са применама (RS-MESTD-Basic Research (BR or ON)-174002)
- NSF grant DMS-1720259
- NSF grant DMS-1729509
Колекције
Институција/група
Mašinski fakultetTY - 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 .