A study of eigenvalue distribution of Hermitian Toeplitz matrix
碩士 === 國立中山大學 === 應用數學系研究所 === 107 === Hermitian Toeplitz matrix arises from many real applications, such as solving differential equations by using finite difference method. In this paper, we consider the convergence rate of solving linear system Ax = b with the Hermitian Toeplitz matrix by using c...
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| Format: | Others |
| Language: | zh-TW |
| Published: |
2019
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| Online Access: | http://ndltd.ncl.edu.tw/handle/7xrky3 |
| Summary: | 碩士 === 國立中山大學 === 應用數學系研究所 === 107 === Hermitian Toeplitz matrix arises from many real applications, such as solving differential
equations by using finite difference method. In this paper, we consider the convergence
rate of solving linear system Ax = b with the Hermitian Toeplitz matrix by using conjugate
gradient method. The convergence rate of conjugate gradient method basically
depends on the condition number on the matrix. We demonstrate the upper bound and
lower bound of eigenvalues of Hermitian Toeplitz matrix. In the mathematical experiments,
we notice that when the size of Hermitian Toeplitz matrix becomes larger, the
distribution of the eigenvalues seems approach the associated distribution function.
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