| EPSRC Reference: |
GR/T08739/01 |
| Title: |
Topics in Matrix Computations |
| Principal Investigator: |
Higham, Professor NJ |
| Other Investigators: |
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| Department: |
Mathematics |
| Organisation: |
University of Manchester, The |
| Scheme: |
Mathematics Small Grant PreFEC |
| Starts: |
01 April 2004 |
Ends: |
31 August 2004 |
Value (£): |
10,239
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Summary on Grant Application Form |
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This work concerns three timely topics in matrix computations on which the investigators intend to collaborate with the proposed VF Profesor Roy Mathias (College of William and Mary, Williamsburg). We will investigate perturbation theory for, and computation of, the eigenvalues and eigenvectors of hyperbolic quadratic eigenvalue problems, for which important applications are in structural mechanics. We will develop algorithms to compute f(A)b, using only matrix vector products, and we will analyze the quality of the approximations they produce. Here A is an nxn matrix, b is an n-vector and f is a function, for instance f(A) = sign(A) as arises in lattice quantum chromodynamics (QCD). We will also investigate the perturbation theory of the generalized polar decomposition A = WS, where W and S are in the automorphism group and Jordan algebra associated with a scalar product product, repectively. We wish to develop sharp bounds for the changes in W and S induced by changes in A, and hence to identify the condition numbers of W and S.
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Key Findings |
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This information can now be found on Gateway to Research (GtR) http://gtr.rcuk.ac.uk
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Potential use in non-academic contexts |
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This information can now be found on Gateway to Research (GtR) http://gtr.rcuk.ac.uk
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Impacts |
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| Description |
This information can now be found on Gateway to Research (GtR) http://gtr.rcuk.ac.uk |
| Summary |
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| Date Materialised |
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Sectors submitted by the Researcher |
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This information can now be found on Gateway to Research (GtR) http://gtr.rcuk.ac.uk
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| Project URL: |
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| Further Information: |
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| Organisation Website: |
http://www.man.ac.uk |