与切比雪夫多项式相关的循环m -对角矩阵

Ahmet Öteles
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引用次数: 0

摘要

在本研究中,我们处理一个$m$带状循环矩阵,一般称为循环$m$-对角矩阵。这种特殊的循环矩阵族在预测、时间序列分析、样条近似、偏微分方程的差分解等许多应用中都有出现。首先基于第一类和第二类Chebyshev多项式,得到了循环m -对角矩阵的特征值和特征向量的表述。然后,我们根据上述多项式给出了该矩阵族的整数幂的有效公式。最后,利用计算机代数系统(CAS)中的maple软件进行了实例说明。
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Circulant $m$-diagonal matrices associated with Chebyshev polynomials
In this study, we deal with an $m$ banded circulant matrix, generally called circulant $m$-diagonal matrix. This special family of circulant matrices arise in many applications such as prediction, time series analysis, spline approximation, difference solution of partial differential equations, and so on. We firstly obtain the statements of eigenvalues and eigenvectors of circulant $m$-diagonal matrix based on the Chebyshev polynomials of the first and second kind. Then we present an efficient formula for the integer powers of this matrix family depending on the polynomials mentioned above. Finally, some illustrative examples are given by using maple software, one of computer algebra systems (CAS).
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