| NSF Org: |
DMS Division Of Mathematical Sciences |
| Recipient: |
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| Initial Amendment Date: | August 17, 2021 |
| Latest Amendment Date: | August 17, 2021 |
| Award Number: | 2110731 |
| Award Instrument: | Standard Grant |
| Program Manager: |
Yuliya Gorb
ygorb@nsf.gov (703)292-2113 DMS Division Of Mathematical Sciences MPS Directorate for Mathematical and Physical Sciences |
| Start Date: | September 1, 2021 |
| End Date: | August 31, 2025 (Estimated) |
| Total Intended Award Amount: | $324,815.00 |
| Total Awarded Amount to Date: | $324,815.00 |
| Funds Obligated to Date: |
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| History of Investigator: |
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| Recipient Sponsored Research Office: |
500 S LIMESTONE LEXINGTON KY US 40526-0001 (859)257-9420 |
| Sponsor Congressional District: |
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| Primary Place of Performance: |
500 S Limestone 109 Kinkead Hall Lexington KY US 40526-0001 |
| Primary Place of
Performance Congressional District: |
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| Unique Entity Identifier (UEI): |
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| Parent UEI: |
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| NSF Program(s): | COMPUTATIONAL MATHEMATICS |
| Primary Program Source: |
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| Program Reference Code(s): |
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| Program Element Code(s): |
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| Award Agency Code: | 4900 |
| Fund Agency Code: | 4900 |
| Assistance Listing Number(s): | 47.049 |
ABSTRACT
The mathematical questions in this project arise in electronic structure calculations in computational materials science, signal processing of brain?computer interfaces in neuroscience and biomedical engineering, among other applications. The questions come in a variety of forms and pose intriguing challenges for mathematical analysis and numerical solutions. This project seeks to advance the state-of-the-art of the analysis and computation. The project's outcome will advance understanding of the mathematical problems and provide tools for researchers and practitioners to perform simulations in less time using advanced models that were previously unavailable. This project will integrate research into teaching and education and will engage students at various levels in computational mathematics and interdisciplinary research.
This project will support one graduate per year in each of the three years of the grant. Technically, this project will focus on an important class of Eigenvector-dependent Nonlinear Eigenvalue Problems NEPv, called affine-linear NEPv (al-NEPv). In an al-NEPv, the coefficient matrix of NEPv poses an affine-linear structure. Origins of al-NEPv include trace-related optimizations such as the trace-ratio optimization for dimension reduction and robust Rayleigh-quotient optimization for handling data uncertainties, among others. The PI plans to conduct systematic analysis and algorithmic development for al-NEPv. The main components of the proposed research are threefold: analysis of al-NEPv, such as a novel geometric description and a variational characterization; new geometric interpretation of the self-consistent field (SCF) iteration for solving al-NEPv, and variants of SCF for handling the local optimal issue and for accelerating the convergence of SCF; availability of a public-domain repository for the collection of NEPv from real-life applications.
This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.
PUBLICATIONS PRODUCED AS A RESULT OF THIS RESEARCH
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