A divide-and-conquer algorithm for a symmetric tri-block-diagonal matrix

We propose a stable and efficient divide-and-conquer algorithm for computing the eigendecomposition of a symmetric tri-block-diagonal matrix. The matrix can be derived from discretizing Laplace operator eigenvalue in some two-dimensional graphs. All numerical results show that our algorithm is compe...

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Bibliographic Details
Main Authors: Nguyen, Binh T., Anh-Duc Luong-Thanh, Nguyen Dinh Thuc, Bui Van Thach
Format: Conference Proceeding
Language:English
Subjects:
Acceleration
Complexity theory
Eigenvalues and eigenfunctions
Laplace equations
Symmetric matrices
Vectors
Vegetation
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Summary:We propose a stable and efficient divide-and-conquer algorithm for computing the eigendecomposition of a symmetric tri-block-diagonal matrix. The matrix can be derived from discretizing Laplace operator eigenvalue in some two-dimensional graphs. All numerical results show that our algorithm is competitive with other methods, such as e.g QR algorithm, Cuppen's divide-and-conquer algorithm. We also show how to improve our algorithm by Fast Multipole Method.
ISSN:1091-0050
1558-058X
DOI:10.1109/SECon.2012.6196898