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research
I am working on calculating a symmetry preserving singular value decomposition (SPSVD), which is a matrix factorization that gives the best symmetric low rank approximation to a set of data. This decomposition has applications in molecular dynamics and face detection. For more information, check my SIMAX paper.
teaching
- Calculus II
http://www.evergreen.loyola.edu/~mishah/MA252-S08/
- Numerical Analysis
http://www.evergreen.loyola.edu/~mishah/MA427-S08/
papers
[4] M. I. Shah and D. C. Sorensen, Best Symmetric Low Rank Approximation via the Symmetry Preserving Singular Value Decomposition, submitted.
[3] M. I. Shah and D. C. Sorensen, A symmetry preserving singular value decomposition, SIAM Journal on Matrix Analysis and Applications, 28 (2006), pp. 749-769.
[2] W. Wriggers, Z. Zhang, M. Shah, and D. C. Sorensen, Simulating nanoscale functional motions of biomolecules, Molecular Simulation, 32 (2006), pp. 803-815.
[1] D. C. Sorensen and M. Shah, Principal component analysis and model reduction for dynamical systems with symmetry constraints, European Control Conference (CDC-ECC), 2005, pp. 2260-2264.
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