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A direct solver for solving systems of linear equations with banded ill-conditioned Toeplitz matrices | ||
| Journal of Mathematical Modeling | ||
| مقاله 5، دوره 10، شماره 4، اسفند 2022، صفحه 453-461 اصل مقاله (156.64 K) | ||
| نوع مقاله: Research Article | ||
| شناسه دیجیتال (DOI): 10.22124/jmm.2022.22278.1965 | ||
| نویسنده | ||
| Nasser Akhoundi* | ||
| School of Mathematics and Computer Science, Damghan University, Damghan, Iran | ||
| چکیده | ||
| In this paper, the banded Toeplitz matrices generated by $f(\theta)=(2(1-\cos(\theta-\tilde{\theta})))^d$ are studied. The function $f$ is a real non-negative function with a zero of order $2d$ at $\tilde{\theta}$ and the generated matrices are ill-conditioned Hermitian positive definite. We show that these banded Toeplitz matrices are similar to the banded real symmetric positive definite Toeplitz matrices that are generated by $f(\theta)=(2(1-\cos(\theta)))^d$. A fast direct solver is proposed to compute the inverse of these real matrices. Numerical experiments show that our proposed method is faster and more stable than the stable Levinson algorithm. | ||
| کلیدواژه‌ها | ||
| Toeplitz matrices؛ fast Toeplitz solver؛ Levinson algorithm | ||
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آمار تعداد مشاهده مقاله: 825 تعداد دریافت فایل اصل مقاله: 441 |
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