### Rayleigh Quotient Iteration in Alpha-eigenvalue Neutron Transport Problems

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Mario Ortega, University of California, Berkeley
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Alpha-eigenvalue problems in neutron transport allow designers to determine the criticality of nuclear systems and the time behavior of neutron flux in a system. Realistic neutron transport calculations require solving systems with hundreds of unknowns in space, direction and energy, creating linear systems with hundreds of thousands of unknowns and demanding the use of high-performance computing. Solving an eigenvalue problem with systems of this size requires the development of specialized techniques. In this poster, we present a Rayleigh quotient iteration approach to solving the alpha-eigenvalue problem and present some results on simple nuclear criticality benchmarks. We also present some mathematical results concerning when the method should converge, the rate of convergence and the possibility of acceleration methods.

**Abstract Author(s): **Mario I. Ortega, Britton Chang, Peter N. Brown, Teresa S. Bailey, Rachel N. Slaybaugh