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
- Differential Equations
http://math.loyola.edu/~mili/MA304-S09/

papers [5] M. I. Shah, Symmetric Eigenfaces, submitted. [4] M. I. Shah and D. C. Sorensen, Best Non-Spherical Symmetric Low Rank Approximation, SIAM Journal on Matrix Analysis and Applications, to appear. [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.