Type of Document	Dissertation
Author	Baker, Christopher Grover
URN	etd-05232008-143350
Title	Riemannian Manifold Trust-Region Methods with Applications TO Eigenproblems
Degree	Doctor of Philosophy
Department	Scientific Computing, Department of
Advisory Committee	Advisor Name Title Kyle Gallivan Committee Co-Chair Pierre-Antoine Absil Committee Co-Chair Anjaneyulu Krothapalli Committee Member Anuj Srivastava Committee Member Gordon Erlebacher Committee Member Yousuff Hussaini Committee Member
Keywords	Riemannian Manifolds Iterative Methods Convergence Theory Numerical Optimization Eigenvalue Problems Trust-Region Methods Riemannian Optimization Optimization on Manifolds
Date of Defense	2008-05-22
Availability	unrestricted
Abstract This thesis presents and evaluates a generic algorithm for incrementally computing the dominant singular subspaces of a matrix. The relationship between the generality of the results and the necessary computation is explored, and it is shown that more efficient computation can be obtained by relaxing the algebraic constraints on the factoriation. The performance of this method, both numerical and computational, is discussed in terms of the algorithmic parameters, such as block size and acceptance threshhold. Bounds on the error are presented along with a posteriori approximations of these bounds. Finally, a group of methods are proposed which iteratively improve the accuracy of computed results and the quality of the bounds.
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