article · 2022

Enhanced matrix function approximation

Eshghi, Nasim, Reichel, Lothar, Spalević, Miodrag

Cited by 0Abstract and details only

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.

Cite this paper

APA 7

Eshghi, N., Reichel, L., & Spalević, M. (2022). Enhanced matrix function approximation.

MLA 9

Eshghi, Nasim, et al. “Enhanced matrix function approximation.” 2022.

Chicago

Eshghi, Nasim, Lothar Reichel, and Miodrag Spalević. 2022. “Enhanced matrix function approximation.”

Harvard

Eshghi, N., Reichel, L. and Spalević, M. (2022) ‘Enhanced matrix function approximation’.

BibTeX

@article{eshghi2022enhanced,
  title = {{Enhanced matrix function approximation}},
  author = {Eshghi, Nasim and Reichel, Lothar and Spalević, Miodrag},
  year = {2022}
}

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