Improving Feast for Real Symmetric Standard Eigenvalue Problems

Date

2024-9-03

Author

Özçoban, Kadir

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Eigenvalue problems may arise from various application areas including Quantum mechanics, Computational Fluid Dynamics, Power Networks, and Machine Learn ing. To solve these problems, several methods for computing all or a batch of eigen values and eigenvectors (i.e. eigenpairs) have been proposed over the years, including both direct and iterative approaches. FEAST is a subspace-based iterative technique that simplifies the computation by projecting the problem onto a lower-dimensional subspace while preserving the eigenpairs. Despite its widespread use, FEAST is not without limitations. One of the most conspicuous problems is that a crucial matrix for the algorithm which is supposed to be orthogonal might lose its orthogonality throughout the iterations because of the well-known floating point errors or the ap proximate methods used to obtain it. This possible issue could cause slower convergence or even spurious eigenvalues, values that do not originally belong to the matrix. In this thesis, new as well as existing methods to improve the stability of the FEAST algorithm are investigated over various eigenvalue spectrum. Additionally, a novel method in which FEAST is preceded with inverse subspace iteration to provide better initial guesses for the algorithm is studied. Moreover, this method is further extended in a Hybrid manner by iterating these two alternatively.

Subject Keywords

Eigenvalue Problem, FEAST, Hybrid Approaches, Sparse Matrix Computations

URI

https://hdl.handle.net/11511/111357

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Graduate School of Natural and Applied Sciences, Thesis