共查询到20条相似文献,搜索用时 78 毫秒
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给出了一种三对角矩阵的特征值和特征向量的算法,利用矩阵方法和对称多项式证明了一些与Lucas数以及第一类Chebyshev多项式有关的三角恒等式. 相似文献
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三对角线阵行列式恒等式及应用 总被引:1,自引:0,他引:1
本文导出了求三对角线阵行列式的显式表示.这个恒等式可应用于研究三对角线阵的逆矩阵和特征值性质以及求某些正交多项式的显式表示,并能由此导出一类有用的恒等式. 相似文献
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三角恒等式的证明是中学三角教学的一个重要内容.在中学里,对较简单的三角恒等式的证明都是通过三角的恒等变换给出的,但是对于本文(五)内所给出的一系列三角恒等式,如果利用三角恒等变换来证明是比较困难的.本文讨论利用代数的方法来证明这类三角恒等式,不仅简单,而且可以获得同一类的三角恒等式的统一证法.我们不仅要会证明这类三角恒等式,而且还 相似文献
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本文提出一类求解特征值问题的下三角预变换方法, 目标是通过相似变换后矩阵下三角元素平方和明显减少、且变换后的特征值及其特征向量较易求解, 使变换后的对角线可作为全体特征值很好的一组初值, 其作用如同对于解方程组找到好的预条件子, 加速迭代收敛. 以二阶PDE 数值计算为例,对于以Laplace 方程为代表的特征波向量组及正交多项式组有广泛的应用前景.
杨辉三角是我国古代数学家的一项重要成就. 本文引入杨辉三角矩阵作为预变换子, 给出一般矩阵用杨辉三角矩阵作为左、右预变换子时变为上三角矩阵的充要条件, 给出了元素为行指标二次多项式的两个矩阵类(三对角线阵与五对角线阵) 中特征值何时保持二次多项式的充要条件, 并应用于构造新的二元PDE 正交多项式. 相似文献
杨辉三角是我国古代数学家的一项重要成就. 本文引入杨辉三角矩阵作为预变换子, 给出一般矩阵用杨辉三角矩阵作为左、右预变换子时变为上三角矩阵的充要条件, 给出了元素为行指标二次多项式的两个矩阵类(三对角线阵与五对角线阵) 中特征值何时保持二次多项式的充要条件, 并应用于构造新的二元PDE 正交多项式. 相似文献
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本文聚焦三角形中的三角恒等式的系统文献研究,对美英早期三角学教科书进行考察,对其中的三角恒等式进行归类,对三角恒等式的证明方法加以梳理,为课堂教学提供素材和思想启迪. 相似文献
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Hongwei Chen 《International Journal of Mathematical Education in Science & Technology》2013,44(2):306-309
A new trigonometric identity derived from factorizations and partial fractions is given. This identity is used to evaluate the Poisson integral via Riemann sum and to establish some trigonometric summation identities. 相似文献
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We obtain some new trigonometric identities and find the corresponding Chebyshev polynomials identities. We also indicate their applications to certain boundary value problems which arise in Mechanics. 相似文献
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Guido Walz 《BIT Numerical Mathematics》1997,37(1):189-201
In this paper we investigate some properties of trigonometric B-splines. We establish a complex integral representation for
these functions, which is in certain analogy to the polynomial case, but the proof of which has to be done in a different
and more complicated way. Using this integral representation, we can prove some identities concerning the evaluation of a
trigonometric B-spline, its derivative and its partial derivative w.r.t. the knots. Finally we show that—in the case of equidistant
knots—the trigonometric B-splines of odd order form a partition of a constant, and therefore the corresponding B-spline curve
possesses the convex-hull property. This is illustrated by a numerical example. 相似文献
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S. A. Obaid 《Applied Mathematics Letters》1989,2(4):367-370
We derive two new trigonometric identities and the corresponding Chebyshev identities. We also obtain new Fibonacci and Lucas Identities. 相似文献
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In this note, we study trigonometric identities involving the angles of an arbitrary triangle and we give algorithms for verifying such identities. 相似文献
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By evaluating a contour integral with the Cauchy residue theorem, we prove a general summation formula on trigonometric sum, which contains several interesting trigonometric identities as special cases. 相似文献
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Wenchang Chu 《Proceedings of the American Mathematical Society》2008,136(1):229-237
The partial fraction decomposition method is explored to establish several interesting trigonometric function identities, which may have applications to the evaluation of classical multiple hypergeometric series, trigonometric approximation and interpolation.
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一类无穷积分的计算公式 总被引:1,自引:1,他引:0
利用分部积分法和L′Hosp ita l法则得到了无穷积分∞∫0sin(βx)xncos(bx)dx(其中正整数n 1,实数β≠0,b 0)的一般计算公式,并且作为副产品得到了三个组合恒等式. 相似文献
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Eric M. Rains 《The Ramanujan Journal》2009,18(3):257-306
In Ann. Math., to appear, 2008, the author proved a number of multivariate elliptic hypergeometric integrals. The purpose of the present note is to explore
more carefully the various limiting cases (hyperbolic, trigonometric, rational, and classical) that exist. In particular,
we show (using some new estimates of generalized gamma functions) that the hyperbolic integrals (previously treated as purely
formal limits) are indeed limiting cases. We also obtain a number of new trigonometric (q-hypergeometric) integral identities as limits from the elliptic level.
The author was supported in part by NSF Grant No. DMS-0401387. 相似文献
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R. Kittappa 《Linear and Multilinear Algebra》1981,10(1):75-82
The conjecture made in 1881 by R. F. Scott on permanents is proved. Two new trigonometric identities are also stated and proved. 相似文献