| EPSRC Reference: |
GR/R22612/01 |
| Title: |
Numerical Analysis of Matrix Functions |
| Principal Investigator: |
Higham, Professor NJ |
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| Department: |
Mathematics |
| Organisation: |
Victoria University of Manchester, The |
| Scheme: |
Standard Research (Pre-FEC) |
| Starts: |
01 February 2001 |
Ends: |
31 January 2004 |
Value (£): |
129,092
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| Information Technologies |
No relevance to Underpinning Sectors |
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Summary on Grant Application Form |
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Functions of a matrix are ubiquitous in applied mathematics. The exponential of a matrix, for example, arises explicitly or implicitly in the solution of differential equations in control theory, nuclear magentic resonance, and geometric integration. Inverse problems in these areas require the matrix logarithm. We plan to make significant advances in the theory and computation of matrix functions, paying careful attention to the needs of practitioners in applications. A major contribution will be to develop a reliable Schur-based method for computing a general function f(A), and provide software. Such a method is currently lacking, but will be of wide use and will, we believe, out-perform many methods that have been suggested for specific functions. We will also develop specialized methods for the matrix exponential, other transcendental functions, and matrix p'th roots. A novel problem arising in lattice quantum chromodynamics will be investigated: how to compute f(A)b without computing f(A), when A is a large, sparse matrix. We will develop structured perturbation theory and corresponding condition numbers and combine them with rounding error analysis to understand the behaviour of our methods in floating point arithmetic.
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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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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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