| EPSRC Reference: |
EP/W018101/1 |
| Title: |
Mixed Precision Symmetric Eigensolvers: Proof of Concept |
| Principal Investigator: |
Tisseur, Professor F |
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| Department: |
Mathematics |
| Organisation: |
University of Manchester, The |
| Scheme: |
Standard Research - NR1 |
| Starts: |
01 July 2022 |
Ends: |
30 June 2023 |
Value (£): |
71,607
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| No relevance to Underpinning Sectors |
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Summary on Grant Application Form |
The numerical solution of algebraic eigenvalue problems is a key technology underpinning many areas of computational science and engineering, including acoustics, aeronautics, control theory, fluid mechanics, population modelling, quantum physics, robotics, and structural engineering. In all these areas, the need for fast and numerically reliable solution of eigenvalue problems arises. The problems can be large so that time to solution can be unacceptably long.
Modern hardware (multicore processors and accelerators such as graphics processing units (GPUs)) increasingly supports half precision floating-point arithmetics. These low precisions provide new opportunities to considerably accelerate linear algebra computations.
The research in this "small grant" proposal is a proof of concept for the next generation of efficient and numerically stable eigensolvers that exploit the different arithmetic precisions of modern hardware while maintaining numerical stability. Our investigation concentrates on the symmetric eigenvalue problem, for which eigenvalues are real with a full set of orthonormal eigenvectors, but any advances will have direct impact on future algorithms for nonsymmetric eigenproblems, generalized eigenproblems, and the singular value decomposition.
The algorithms will be developed as prototypes in MATLAB, using simulated half precision. Their numerical stability will be analyzed as well as their efficiency in terms of arithmetic costs and communications costs so as to determine which one(s) should be fully implemented in state of the art numerical linear algebra libraries such as the freely available matrix algebra on GPU and multicore architectures (MAGMA) library.
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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 |
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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 |