CHEBYSHEV POLYNOMIALS WITH ZEROS ON THE CIRCLE AND RELATED TOPICS

Maergoiz L. S.; Rybakova N. N.

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CHEBYSHEV POLYNOMIALS WITH ZEROS ON THE CIRCLE AND RELATED TOPICS

机译：带圆角的切比雪夫多项式和相关主题

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A description is given for the Chebyshev monic polynomial T-n* of degree n with zeros on the circle and with the smallest deviation from zero on an arc. The construction of the extremal trigonometric polynomial of order n/2 associated with T-n* is investigated and dual extremal problems are studied. The results are applied to estimating an optimal error for extrapolation from a finite set in the Wiener class.

机译：给出了度数为n的切比雪夫单项多项式T-n *的描述，圆上为零，圆弧上与零的偏差最小。研究了与T-n *相关的n / 2阶极值三角多项式的构造，并研究了对偶极值问题。将结果应用于从Wiener类的有限集中估计最佳外推误差。

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《St. Petersburg mathematical journal》 |2014年第6期|共15页
作者
Maergoiz L. S.; Rybakova N. N.;
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正文语种 eng
中图分类数学;
关键词
Polynomial of smallest deviation from zero; Chebyshev alternance;

机译：与零的最小偏差的多项式;契比雪夫交替;

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专利

1. CHEBYSHEV POLYNOMIALS WITH ZEROS ON THE CIRCLE AND RELATED TOPICS [J] . Maergoiz L. S., Rybakova N. N. St. Petersburg mathematical journal . 2014,第6期

机译：带圆角的切比雪夫多项式和相关主题
2. 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
3. Numerical computation of the number of zeros of real polynomials in the open unit disk using a Chebyshev polynomials representation [J] . Gleyse B., Larabi A. Applied mathematics letters . 2011,第5期

机译：使用Chebyshev多项式表示的开放单元盘中实多项式零数目的数值计算。
4. Optimal tracking and disturbance rejection with invariant zeros on the unit circle: a polynomial spectral factorization design [C] . Drilon Bunjaku, Jovan D. Stefanovski, Georgi M. Dimirovski, IFAC World Congress . 2018

机译：单位圆上不变零的最佳跟踪和干扰抑制：多项式谱分解设计
5. Zero Distribution of Binomial Combinations of Chebyshev Polynomials of the Second Kind [D] . Al Hamdani, Summer F. 2021

机译：第二种芝双思河豚多项式的二项组合的零分布
6. The Number of Zeros of a Polynomial in a Circle [O] . Morris Marden 1948

机译：圆中多项式的零点数目
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. Zeros of Certain Linear Combinations of Chebyshev Polynomials [R] . Bavinck, H. 1995

机译：Chebyshev多项式的某些线性组合的零点

CHEBYSHEV POLYNOMIALS WITH ZEROS ON THE CIRCLE AND RELATED TOPICS

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