Document Details

Document Type : Thesis 
Document Title :
FINE SPECTRAL ANALYSIS FOR ISGEOMETRIC APPROXIMATION OF DIFFERENTIAL OPERATORS
التحليل الطيفي المحسن لتقريبات المؤثرات التفاضلية المتماثلة
 
Subject : Faculty of Sciences 
Document Language : Arabic 
Abstract : It is always fascinating to develop efficient algorithms to compute the eigenvalues or generalized eigenvalues. Computing the eigenvalues of large matrices are computationally expensive. However, when talking about structured matrices, whose eigenvalues are not random but follow some regular pattern, it is possible to design computationally efficient algorithms to find eigenvalues or generalized eigenvalues. We have developed an algorithm to extrapolate the generalized eigenvalues of a given pair of Hermitian matrices that have Toeplitz or Quasi-Toeplitz structure. We collect information of eigenvalues of much smaller matrices to compute the eigenvalues of much larger matrices. The central part of our proposed algorithm is the expansion of eigenvalue with unknown coefficients. We compute the coefficients, over a grid, from different sets of eigenvalues of different size matrices. After the computation of the coefficients, we can extrapolate the eigenvalues for much larger matrices. The generating functions of Toeplitz matrices play an important role in the algorithm. We have tested our algorithm for some self-designed examples of Hermitian Toeplitz matrices to show the correctness and efficiency of our proposed algorithm. Finally, we apply isogeometric analysis (IgA) to discretize a second order boundary value problem with Dirichlet boundary conditions and compute the associated generalized eigenvalues. The IgA discretized matrices are not Toeplitz due to the implementation of boundary conditions while our algorithm works well in this case. 
Supervisor : Dr. Dalal Adnan Amer Maturi 
Thesis Type : Master Thesis 
Publishing Year : 1439 AH
2018 AD 
Co-Supervisor : Prof.Dr. Eman salem Al-Aidarous 
Added Date : Wednesday, February 14, 2018 

Researchers

Researcher Name (Arabic)Researcher Name (English)Researcher TypeDr GradeEmail
دينا عبدالله الرحيليAlrehaili, Dina AbdullahResearcherMaster 

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