共查询到18条相似文献,搜索用时 78 毫秒
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利用多项式因式分解的逆变换,结合循环矩阵和切比雪夫多项式的特殊结构,首先研究第三类和第四类切比雪夫多项式的通项公式,并给出第三类、第四类切比雪夫多项式的关于行首加r尾r右循环矩阵和行尾加r首r左循环矩阵的行列式的显式表达式,最后给出算法实施步骤. 相似文献
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张曦李江华张哲 《数学的实践与认识》2022,(9):276-280
切比雪夫多项式在各个领域都有广泛的研究,如:群论,密码学和偏微分方程等.主要利用指数和上界证明一类由切比雪夫多项式所生成序列的低差异性,从而说明其均匀分布性质. 相似文献
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谷峰 《数学的实践与认识》2010,40(20)
提出了一个仅使用基本运算加、减和移位计算切比雪夫多项式的坐标旋转算法,证明了收敛性,讨论了误差估计.算法编码占用空间很小,适合在微计算系统中使用. 相似文献
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记 Tn( x) =cos( narccosx) ,这是一个首项系数为 2 n- 1的关于 x的 n次多项式 ,称为切比雪夫多项式 .在函数逼近论中 ,切比雪夫用连续函数的方法证明了一个基本结果 :定理 1 (切比雪夫 ) 记Ωn={f( x) | f( x) =xn+ an- 1xn- 1+… + a1x+ a0 ,a0 ,a1,… ,an- 1∈R},则对任意 f( x)∈ Ωn,都有 max- 1≤ x≤ 1| f( x) |≥ 12 n- 1,且等号成立当且仅当 f( x) =12 n- 1Tn( x) .容易证明定理 1等价于下面的 :定理 2 记Mn={f ( x) | f ( x) =anxn+… + a1x+ a0 ,a0 ,a1,… ,an∈ R ,且当 - 1≤ x≤ 1时 ,| f ( x) |≤ 1 },则对任意 f( x)∈ … 相似文献
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给出了三对角行列式的几种算法,利用三对角行列式证明了两类Chebyshev多项式的几种显式. 相似文献
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利用初等方法研究Chebyshev多项式的性质,建立了广义第二类Chebyshev多项式的一个显明公式,并得到了一些包含第一类Chebyshev多项式,第一类Stirling数和Lucas数的恒等式. 相似文献
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Roman Witu?a 《Journal of Mathematical Analysis and Applications》2006,324(1):321-343
In this paper some new properties and applications of modified Chebyshev polynomials and Morgan-Voyce polynomials will be presented. The aim of the paper is to complete the knowledge about all of these types of polynomials. 相似文献
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Bojan Orel 《Journal of Computational and Applied Mathematics》2012,236(7):1753-1765
An efficient construction of two non-classical families of orthogonal polynomials is presented in the paper. The so-called half-range Chebyshev polynomials of the first and second kinds were first introduced by Huybrechs in Huybrechs (2010) [5]. Some properties of these polynomials are also shown. Every integrable function can be represented as an infinite series of sines and cosines of these polynomials, the so-called half-range Chebyshev-Fourier (HCF) series. The second part of the paper is devoted to the efficient computation of derivatives and multiplication of the truncated HCF series, where two matrices are constructed for this purpose: the differentiation and the multiplication matrix. 相似文献
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主要研究勒让德多项式与契贝谢夫多项式之间的关系的性质,利用生成函数和函数级数展开的方法,得出了勒让德多项式与契贝谢夫多项式之间的一个重要关系,这对勒让德多项式与契贝谢夫多项式的研究有一定的推动作用. 相似文献
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M. Abreu D. Labbate R. Salvi N. Zagaglia Salvi 《Linear algebra and its applications》2008,429(1):367-375
In this paper we investigate generalized circulant permutation matrices of composite order. We give a complete characterization of the order and the structure of symmetric generalized k-circulant permutation matrices in terms of circulant and retrocirculant block (0, 1)-matrices in which each block contains exactly one or two entries 1. In particular, we prove that a generalized k-circulant matrix A of composite order n = km is symmetric if and only if either k = m − 1 or k ≡ 0 or k ≡ 1 mod m, and we obtain three basic symmetric generalized k-circulant permutation matrices, from which all others are obtained via permutations of the blocks or by direct sums. Furthermore, we extend the characterization of these matrices to centrosymmetric matrices. 相似文献
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Igor Rivin 《Proceedings of the American Mathematical Society》2005,133(5):1299-1305
We define a class of multivariate Laurent polynomials closely related to Chebyshev polynomials and prove the simple but somewhat surprising (in view of the fact that the signs of the coefficients of the Chebyshev polynomials themselves alternate) result that their coefficients are non-negative. As a corollary we find that and are positive definite functions. We further show that a Central Limit Theorem holds for the coefficients of our polynomials.
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Yun Fan 《Linear and Multilinear Algebra》2018,66(10):2119-2137
Double circulant matrices are introduced and studied. By a matrix-theoretic method, the rank r of a double circulant matrix is computed, and it is shown that any consecutive r rows of the double circulant matrix are linearly independent. As a generalization, multiple circulant matrices are also introduced. Two questions on square double circulant matrices are posed. 相似文献
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Karl Dilcher Kenneth B. Stolarsky 《Transactions of the American Mathematical Society》2005,357(3):965-981
We show that the resultants with respect to of certain linear forms in Chebyshev polynomials with argument are again linear forms in Chebyshev polynomials. Their coefficients and arguments are certain rational functions of the coefficients of the original forms. We apply this to establish several related results involving resultants and discriminants of polynomials, including certain self-reciprocal quadrinomials.