A restarted Lanczos approximation to functions of a symmetric matrix
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Description
In this paper, we investigate a method for restarting the Lanczos method for approximating the matrix-vector product f(A)b, where A ∈ ℝn×n is a symmetric matrix. For analytic f we derive a novel restart function that identifies the error in the Lanczos approximation. The restart procedure is then generated by a restart formula using a sequence of these restart functions. We present an error bound for the proposed restart scheme. We also present an error bound for the restarted Lanczos approximation of f(A)b for symmetric positive definite A when f is in a particular class of completely monotone functions. We illustrate for some important matrix function applications the usefulness of these bounds for terminating the restart process once the desired accuracy in the matrix function approximation has been achieved.
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ID Code: | 8011 | ||
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Item Type: | Contribution to Journal (Journal Article) | ||
Refereed: | Yes | ||
ORCID iD: |
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Measurements or Duration: | 18 pages | ||
Keywords: | Error Bounds, Fractional Poisson Equation, Gaussian Markov Random Fields, Krylov Subspace Methods, Matrix Functions, Stieltjes Transforms | ||
DOI: | 10.1093/imanum/drp003 | ||
ISSN: | 0272-4979 | ||
Pure ID: | 32189478 | ||
Divisions: | Past > QUT Faculties & Divisions > Faculty of Science and Technology Past > QUT Faculties & Divisions > Science & Engineering Faculty Current > Research Centres > Australian Research Centre for Aerospace Automation |
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Copyright Owner: | Consult author(s) regarding copyright matters | ||
Copyright Statement: | This work is covered by copyright. Unless the document is being made available under a Creative Commons Licence, you must assume that re-use is limited to personal use and that permission from the copyright owner must be obtained for all other uses. If the document is available under a Creative Commons License (or other specified license) then refer to the Licence for details of permitted re-use. It is a condition of access that users recognise and abide by the legal requirements associated with these rights. If you believe that this work infringes copyright please provide details by email to qut.copyright@qut.edu.au | ||
Deposited On: | 07 Jun 2007 00:00 | ||
Last Modified: | 15 Apr 2024 10:08 |
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