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Rayleigh quotient optimizations and eigenvalue problems

PDE and Applied Math Seminar

Speaker: Zhaojun Bai, UCD
Location: 2112 MSB
Start time: Thu, Nov 16 2017, 4:10PM

Many computational science and data analysis techniques lead to optimizing Rayleigh-Quotient (RQ) and RQ-type objective functions, such as computing excitation states (energies) of electronic structures, robust classification to handle uncertainty and constrained data clustering to incorporate a prior information. In this talk, we will discuss origins of some RQ optimizations, variational principles, and reformulations to algebraic linear and nonlinear eigenvalue problems. We will show how to exploit underlying properties of eigenvalue problems for designing eigensolvers, and illustrate the efficacy of these solvers in electronic structure calculations and constrained image segmentation.