On the Bezoutian matrix for Chebyshev polynomials

Yang Z.; Cui B.

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On the Bezoutian matrix for Chebyshev polynomials

机译：关于Chebyshev多项式的Bezoutian矩阵

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摘要

In the present paper a Bezoutian-type matrix relative to Chebyshev polynomials of the second kind is introduced by the form of generating function. A Barnett-type factorization formula and a triangular-type formula are obtained for this generalized Bezout matrix, which generalize the corresponding results for classical Bezout matrix. Two numerical examples are given to illustrate the correctness of our results.

机译：在本文中，通过生成函数的形式介绍了相对于第二类Chebyshev多项式的Bezoutian型矩阵。对于该广义Bezout矩阵，获得了Barnett型分解公式和三角型公式，从而对经典Bezout矩阵的相应结果进行了概括。给出两个数值例子来说明我们结果的正确性。

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《Applied mathematics and computation》 |2012年第3期|共10页
作者
Yang Z.; Cui B.;
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正文语种 eng
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关键词
Barnett-type factorization; Bezoutian matrix; Chebyshev polynomials; Triangular-type formula;

机译：Barnett型分解;Bezoutian矩阵;Chebyshev多项式;三角型公式;

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专利

1. On the Bezoutian matrix for Chebyshev polynomials [J] . Yang Z., Cui B. Applied mathematics and computation . 2012,第3期

机译：关于Chebyshev多项式的Bezoutian矩阵
2. Polynomial Bezoutian matrix with respect to a general basis [J] . Yang ZH. Linear Algebra and its Applications . 2001,第1a3期

机译：关于一般基础的多项式Bezoutian矩阵
3. Numerical experiments on the accuracy of the Chebyshev-Frobenius companion matrix method for finding the zeros of a truncated series of Chebyshev polynomials [J] . John P. Boyd, Daniel H. Gaily Journal of Computational and Applied Mathematics . 2007,第1期

机译：Chebyshev-Frobenius伴随矩阵方法用于查找舍宾谢夫多项式截断序列的零点的精度的数值实验
4. The Transformation Matrix of Chebyshev III - Bernstein Polynomial Basis [C] . Abedallah Rababah, Ayman AL-Shbool International Conference of Numerical Analysis and Applied Mathematics . 2016

机译：Chebyshev III - Bernstein多项式的变换矩阵
5. Chebyshev polynomial based finite element stiffness matrix formulation. [D] . Sivess, Andrew Gregory. 2005

机译：基于切比雪夫多项式的有限元刚度矩阵公式。
6. Sums of finite products of Chebyshev polynomials of the second kind and of Fibonacci polynomials [O] . Taekyun Kim, Dae San Kim, Dmitry V. Dolgy, -1

机译：第二类Chebyshev多项式和Fibonacci多项式的有限积的和
7. Numerical experiments on the accuracy of the Chebyshev–Frobenius companion matrix method for finding the zeros of a truncated series of Chebyshev polynomials [O] . Boyd John P., Gally Daniel H. 2007

机译：Chebyshev-Frobenius伴随矩阵方法用于查找舍宾谢夫多项式截断序列的零点的精度的数值实验
8. Chebyshev Coefficients for Chebyshev Polynomials of Orders 12 and 24 under the General Linear Transformation [R] . Isabelle Arsham 1956

机译：一般线性变换下12阶和24阶Chebyshev多项式的Chebyshev系数

On the Bezoutian matrix for Chebyshev polynomials

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