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同时求多项式全部零点的一族快速并行迭代和区间迭代(Ⅱ) 总被引:3,自引:0,他引:3
本文对[1]所提出的一族同时求多项式全部零点的并行迭代兼区间迭代加以进一步的发展。首先,作为纯粹的并行迭代法,我们在§2把每步并行迭代扩展为q个并行子步,这样得到的并行迭代法对只有单零点的多项式的全部零点的收敛是q(p 1)阶的。值得注意的是,在这里阶的提高大大超过了每步计算代价的增加,例如,当q=2时,每步 相似文献
3.
黄开斌 《高等学校计算数学学报》1983,(3)
如所周知,除非多项式的系数被精确地给出,并能用字长为t的机器数精确地表示出来,我们至多只能根据原多项式的某一扰动多项式着手计算,后者的系数是原多项式系数的t位近似。即使可以无误差输入,按向后误差分析的观点,计算原多项式零点时舍入误差的累积影响可归结为对原多项式系数的等价扰动,从而必须研究多项式的零点对系数有微小相对扰动时的灵敏性。即,必须研究多项式零点的性态。 相似文献
4.
通过区间值函数和实值函数的关系探讨了区间相关性导致的区间扩张的问题,给出了保证区间计算获得足够精度的计算方法;提出了基于单元的子区间摄动有限元计算方法,并给出了提高计算效率的一些方法和获得较好计算精度时的子区间数目的近似计算公式.结合工程实例,基于单元的子区间有限元方法和抗滑稳定性分析方法给出了稳定性的区间范围,为更合理地估计和评价结构的抗滑稳定性提供一定的依据. 相似文献
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关于Gauss-Turán求积公式的注记 总被引:2,自引:0,他引:2
1.引言 设w(x)是区间[-1,1]上的权函数,N是自然数集,X1,…,Xn(n∈N)是对应于权函数w(x)的n次正交多项式的零点,则具有最高代数精度2n-1,其中Πn表示所有次数≤n的多项式空间. 1950年,Turan[1]将上述经典的Gauss求积公式予以推广,证明了,若 相似文献
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KNA 算法是计算多项式全部零点的单纯同伦算法。当多项式只有单零点时,本文证明。当计算达到某一深度后,KNA 算法是单调的,并且用多项式的系数给出开始出现单词性的深度。 相似文献
7.
Faber多项式通常被用来研究单叶函数的性质,同时也提供了用多项式逼近区域内的解析函数的一个有价值的工具.本文给出一个关于∑类单叶函数的Faber多项式递推公式,并由此得到计算Faber系数的新公式,在一定情形下,它比已有的公式更为简单. 相似文献
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A.H.Stroud给出了关于二元m^2点2m-1次求积公式存在性的充分条件,即两个m次直交多项式P1(x,y)和p2(x,y)存在m^2个不同的公共零点,并且都不是无穷远点。本文用不变因子的方法给出了当m=2时这种直交多项式对的一种选取方法.另外,本文最后给出了一些2m-1次积分公式. 相似文献
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给出了基于n次Chebyshev多项式零点的Gauss型Hermite求积公式中Cotes数的明显表达式及其当n→∞时的渐近性质.此即给出了P.Turan问题26的解. 相似文献
11.
鉴于传统预测方法一直基于“点”来衡量时间序列数据,然而现实生活中在给定的时间段内许多变量是有区间限制的,点值预测会损失波动性信息。因此,本文提出了一种基于混合区间多尺度分解的组合预测方法。首先,建立区间离散小波分解方法(IDWT)、区间经验模态分解方法(IEMD)和区间奇异普分析方法(ISSA)。其次,用本文构建的IDWT、IEMD和ISSA对区间时间序列进行多尺度分解,从而得到区间趋势序列和残差序列。然后,用霍尔特指数平滑方法(Holt's)、支持向量回归(SVR)和BP神经网络对区间趋势序列和残差序列进行组合预测得到三种分解方法下的区间时间序列预测值。最后,用BP神经网络对各预测结果进行集成得到区间时间序列最终预测值。同时,为证明模型的有效性进行了AQI空气质量的实证预测分析,结果表明,本文所提出基于混合区间多尺度分解的组合预测方法具有较高的预测精度和良好的适用性。 相似文献
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We describe how to perform the backward error analysis for the approximation of \(\exp (A)v\) by \(p(s^{-1}A)^sv\), for any given polynomial p(x). The result of this analysis is an optimal choice of the scaling parameter s which assures a bound on the backward error, i.e. the equivalence of the approximation with the exponential of a slightly perturbed matrix. Thanks to the SageMath package expbea we have developed, one can optimize the performance of the given polynomial approximation. On the other hand, we employ the package for the analysis of polynomials interpolating the exponential function at so called Leja–Hermite points. The resulting method for the action of the matrix exponential can be considered an extension of both Taylor series approximation and Leja point interpolation. We illustrate the behavior of the new approximation with several numerical examples. 相似文献
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数值积分中的Newton-Cotes公式余项中介点当积分区间长度趋于零时满足确定的极限关系式,当此关系式严格成立时,证明了被积函数是次数不超过某个常数的多项式函数. 相似文献
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The zero set of one general multivariate exponential polynomial with interval coefficients is enclosed by unions and intersections of closed half-spaces. Tighter enclosures are derived in the bivariate case. Common zeros of polynomial systems can be located by an appropriate intersection of these enclosure sets in an appropriate space. The resulting domains are directly brought into polynomial equation solvers. 相似文献
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Takayuki Shiohama Masanobu Taniguchi 《Annals of the Institute of Statistical Mathematics》2001,53(1):142-158
Integral functional of the spectral density of stationary process is an important index in time series analysis. In this paper we consider the problem of sequential point and fixed-width confidence interval estimation of an integral functional of the spectral density for Gaussian stationary process. The proposed sequential point estimator is based on the integral functional replaced by the periodogram in place of the spectral density. Then it is shown to be asymptotically risk efficient as the cost per observation tends to zero. Next we provide a sequential interval estimator, which is asymptotically efficient as the width of the interval tends to zero. Finally some numerical studies will be given. 相似文献
16.
Ghislain Franssens 《Advances in Computational Mathematics》1999,10(3-4):367-388
A new C
∞ interpolant is presented for the univariate Hermite interpolation problem. It differs from the classical solution in that
the interpolant is of non‐polynomial nature. Its basis functions are a set of simple, compact support, transcendental functions.
The interpolant can be regarded as a truncated Multipoint Taylor series. It has essential singularities at the sample points,
but is well behaved over the real axis and satisfies the given functional data. The interpolant converges to the underlying
real‐analytic function when (i) the number of derivatives at each point tends to infinity and the number of sample points
remains finite, and when (ii) the spacing between sample points tends to zero and the number of specified derivatives at each
sample point remains finite.
A comparison is made between the numerical results achieved with the new method and those obtained with polynomial Hermite
interpolation. In contrast with the classical polynomial solution, the new interpolant does not suffer from any ill conditioning,
so it is always numerically stable. In addition, it is a much more computationally efficient method than the polynomial approach.
This revised version was published online in June 2006 with corrections to the Cover Date. 相似文献
17.
Summary. We investigate splines from a variational point of view, which have the following properties: (a) they interpolate given
data, (b) they stay nonnegative, when the data are positive, (c) for a given integer they minimize the functional for all nonnegative, interpolating . We extend known results for to larger , in particular to and we find general necessary conditions for solutions of this restricted minimization problem. These conditions imply that
solutions are splines in an augmented grid. In addition, we find that the solutions are in and consist of piecewise polynomials in with respect to the augmented grid. We find that for general, odd there will be no boundary arcs which means (nontrivial) subintervals in which the spline is identically zero. We show also
that the occurrence of a boundary arc in an interval between two neighboring knots prohibits the existence of any further
knot in that interval. For we show that between given neighboring interpolation knots, the augmented grid has at most two additional grid points. In
the case of two interpolation knots (the local problem) we develop polynomial equations for the additional grid points which
can be used directly for numerical computation. For the general (global) problem we propose an algorithm which is based on
a Newton iteration for the additional grid points and which uses the local spline data as an initial guess. There are extensions
to other types of constraints such as two-sided restrictions, also ones which vary from interval to interval. As an illustration
several numerical examples including graphs of splines manufactured by MATLAB- and FORTRAN-programs are given.
Received November 16, 1995 / Revised version received February 24, 1997 相似文献
18.
Wayne A. Johnson 《Discrete Mathematics》2018,341(5):1237-1243
We consider the exponential generating function whose coefficients encode the dimensions of irreducible highest weight representations which lie on a given ray in the dominant chamber of the weight lattice. This formal power series can be considered as an exponential version of the Hilbert series of a flag variety. In this context, we compute a simple closed form for the exponential generating function in terms of finitely many differential operators and the Stirling polynomials. We prove that this series converges to a product of a rational polynomial and an exponential, and that, by summing the constant term and linear coefficient of this polynomial, we recover the dimension of the representation. 相似文献
19.
Summary.
This paper presents a method to recover
exponential accuracy at all points (including at the
discontinuities themselves), from the knowledge
of an approximation to the
interpolation polynomial (or trigonometrical polynomial).
We show that if we are given the collocation point values
(or a highly accurate approximation) at the Gauss
or Gauss-Lobatto points,
we can reconstruct an uniform exponentially convergent
approximation to the function in any sub-interval
of analyticity. The proof covers the cases of Fourier,
Chebyshev, Legendre, and more
general Gegenbauer collocation methods.
A numerical example is also provided.
Received
July 17, 1994 / Revised version received December 12, 1994 相似文献
20.
We present a new cubature formula in the triangle which exactly integrates polynomials up to degree 6, using only 11 points. The formula was computed by starting with a 12 point cubature formula and applying the reduced basis method to drive one of the weights to zero, resulting in an 11 point formula with positive weights and no points outside the triangle. This improves upon the previously best known positive inside formulas, which have 12 or more points. The lower bound on the number of points for a degree 6 cubature formula in the triangle is 10, which to date has only been obtained by allowing some of the points to be outside the triangle. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献