| EPSRC Reference: |
EP/Y008200/1 |
| Title: |
Reliable and efficient tensor sketching algorithms using structured random matrices |
| Principal Investigator: |
Al Daas, Dr H |
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| Department: |
Scientific Computing Department |
| Organisation: |
STFC Laboratories (Grouped) |
| Scheme: |
Standard Research - NR1 |
| Starts: |
01 January 2024 |
Ends: |
31 December 2024 |
Value (£): |
33,853
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| No relevance to Underpinning Sectors |
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Summary on Grant Application Form |
Randomised linear algebra is an exciting branch of computational mathematics. Randomised linear algebra has had a profound impact in a number of applications where large-scale matrix computation is required; randomised low-rank approximation of matrices is a primary example. In most algorithms in randomised linear algebra, a key idea is to perform a randomised sketch of the matrix.
This project aims to develop efficient techniques for sketching a large-scale matrix or (high-order) tensor. The sketches have a tensor structure that allows them to be applied faster than unstructured (e.g. Gaussian) sketches, while maintaining sufficient randomness that allows algorithms to succeed with high probability. We will establish theoretical justifications for such sketches and identify limitations (if any), so that we can make theoretically justified recommendations on when such sketches should be employed. We expect the new sketch to be competitive in many settings.
We will keep a close eye on applications, in particular in problems involving tensors. A specific application we will investigate is rounding tensors in the tensor-train (TT) format, which is a key computation required when manipulating TT tensors, a popular decomposition for compressing tensors that are large scale and high order. In addition to employing the new sketch, we aim to devise efficient and stable algorithms for rounding.
We will implement the new sketches and algorithms in MATLAB and Fortran, and make the codes publicly available. The Fortran code will be part of RAL's HSL Mathematical Software 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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