| EPSRC Reference: |
GR/L76532/01 |
| Title: |
NUMERICAL ANALYSIS OF THE GENERALIZED EIGENVALUE PROBLEM |
| Principal Investigator: |
Higham, Professor NJ |
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| Department: |
Mathematics |
| Organisation: |
Victoria University of Manchester, The |
| Scheme: |
Standard Research (Pre-FEC) |
| Starts: |
01 January 1998 |
Ends: |
31 December 2000 |
Value (£): |
118,018
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| No relevance to Underpinning Sectors |
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Summary on Grant Application Form |
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The generalized eigenvalue problem (GEP) is a fundamental problem arising in many applications in science and engineering. There is a pressing need for numerical methods to solve the problem reliably and efficiently and for analytic techniques to measure the sensitivity of the problem and the quality of computed solutions. We propose to develop new perturbation theory leading to new backward and forward error bounds and condition numbers for the GEP. We place particular emphasis on respecting structure in the coefficient matrices and on obtaining bounds that are efficiently computable and hence can be included in library software. We also wish to develop new algorithmic techniques and improvements to existing algorithms that will enable solutions to the GEP to be computed faster and more accurately. Specifically, we intend to improve the deflation criteria in the QZ algorithm, investigate iterative refinement of approximate solutions, analyse the shift and invert strategy for iterative solvers, and develop new techniques for the important quadratic eigenvalue problem.
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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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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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