PROPERTY MATRICES IDENTIFICATION OF UNBOUNDED MEDIUM FROM UNIT-IMPULSE RESPONSE FUNCTIONS USING LEGENDRE POLYNOMIALS: FORMULATION     

A. PARONESSO  J. P. WOLF 《地震工程与结构动力学》1996,25(11):1231-1245

A systematic procedure to construct the (symmetric) static-stiffness, damping and mass matrices representing the unbounded medium is presented addressing the unit-impulse response matrix corresponding to the degrees of freedom on the structure–medium interface. The unit-impulse response matrix is first diagonalized which then permits each term to be modelled independently from the others using expansions in a series of Legendre polynomials in the time domain. This leads to a rational approximation in the frequency domain of the dynamic-stiffness coefficient. Using a lumped-parameter model which provides physical insight the property matrices are constructed.  相似文献   

Zn上的k次不可约多项式与k阶Carmichael数     

覃仕霞 《成都信息工程学院学报》2010,25(5):557-560

设n是合数,如果对一切f（x）∈Zn[x]都满足f（x）nk≡f（x）mod（n,r（x））,那么就称n是模r（x）的k阶Carmichael数,这里r（x）是Zn[x]上的k次首一不可约多项式,用Ck,r（x）表示所有这种数的集合,并且定义Ck=Ur（x）Ck,r（x）.k阶Carmichael数,当k=4时,已证明了n=pq,p,q是不同的奇素数,p2-1,q3-1均整除n4-1,则n∈C4.主要目的是将k=4时得出的结论推广到k≥4的一般情形,利用孙子定理,通过构造Zn上的首一k次不可约多项式f（x）的方法,得出：在k≥4时,设n=pq,如果k=2m,m≥2,pm-1,q2m-1-1均整除nk-1,则n∈Ck;如果k=2m＋1,m≥2,pm-1,pm＋1-1,q2m-1均整除nk-1,则n∈Ck.  相似文献   

Bi-cubic interpolation for shift-free pan-sharpening     

《ISPRS Journal of Photogrammetry and Remote Sensing》2013

Most of pan-sharpening techniques require the re-sampling of the multi-spectral (MS) image for matching the size of the panchromatic (Pan) image, before the geometric details of Pan are injected into the MS image. This operation is usually performed in a separable fashion by means of symmetric digital low-pass filtering kernels with odd lengths that utilize piecewise local polynomials, typically implementing linear or cubic interpolation functions. Conversely, constant, i.e. nearest-neighbour, and quadratic kernels, implementing zero and two degree polynomials, respectively, introduce shifts in the magnified images, that are sub-pixel in the case of interpolation by an even factor, as it is the most usual case. However, in standard satellite systems, the point spread functions (PSF) of the MS and Pan instruments are centered in the middle of each pixel. Hence, commercial MS and Pan data products, whose scale ratio is an even number, are relatively shifted by an odd number of half pixels. Filters of even lengths may be exploited to compensate the half-pixel shifts between the MS and Pan sampling grids. In this paper, it is shown that separable polynomial interpolations of odd degrees are feasible with linear-phase kernels of even lengths. The major benefit is that bi-cubic interpolation, which is known to represent the best trade-off between performances and computational complexity, can be applied to commercial MS + Pan datasets, without the need of performing a further half-pixel registration after interpolation, to align the expanded MS with the Pan image.  相似文献   

切比雪夫多项式拟合卫星轨道与钟差的精度分析     

严丽  李萌 《测绘科学》2013,38(3):59-62

利用切比雪夫多项式拟合卫星轨道,用经验统计法确定轨道不同弧段数据的满足精度要求的拟合阶数区间,发现非最佳拟合阶数会引入较大的拟合噪声,因此在精密计算时应选择最佳拟合阶数。本文用此多项式拟合卫星钟差,能达到内插钟差同等的精度,而且与拉格朗日滑动内插相比,拟合残差序列分布更好,计算效率更高;提出利用残差自相关进行精度评定的方法,当精度变化微小时相比一般的精度评定方法具有明显优势。  相似文献   

Second kind Chebyshev operational matrix algorithm for solving differential equations of Lane–Emden type     

《New Astronomy》2013

In this paper, we present a new second kind Chebyshev (S2KC) operational matrix of derivatives. With the aid of S2KC, an algorithm is described to obtain numerical solutions of a class of linear and nonlinear Lane–Emden type singular initial value problems (IVPs). The idea of obtaining such solutions is essentially based on reducing the differential equation with its initial conditions to a system of algebraic equations. Two illustrative examples concern relevant physical problems (the Lane–Emden equations of the first and second kind) are discussed to demonstrate the validity and applicability of the suggested algorithm. Numerical results obtained are comparing favorably with the analytical known solutions.  相似文献   

车贝雪夫多项式约简算法的研究   总被引：4，自引：0，他引：4  

朱应珍  黄永玉 《气象》2000,26(1):25-29

解释了车贝雪夫多项式化整计算通用算法中关于化整后的车贝雪夫多项式约简处理的技术原理,给出了一种可快速实现多项式约简处理的实用求算方法。  相似文献   

On the theory of Chebyshev polynomials in wave-equation migration     

Panos G. Kelamis 《Geophysical Journal International》1988,94(3):421-426

  相似文献   

关于超越亚纯函数f(z)的微分多项式φ(z)f~2(z)f’(z)—1的零点     

张庆德 《成都信息工程学院学报》1992,(4)

本文证明,其中,f(z)为超越亚纯函数,ψ(z)为非零亚纯函数,使得T(r,ψ)=S(r,f),其中,S(r,f)表示O{T(r,f)}(r→+∞),至多除去一个线性测度有限的r集。  相似文献   

A universal spectral analytical method for digital terrain modeling     

I. V. Florinsky  A. N. Pankratov 《International journal of geographical information science》2016,30(12):2506-2528

There are three major mathematical problems in digital terrain analysis: (1) interpolation of digital elevation models (DEMs); (2) DEM generalization and denoising; and (3) computation of morphometric variables through calculating partial derivatives of elevation. Traditionally, these three problems are solved separately by means of procedures implemented in different methods and algorithms. In this article, we present a universal spectral analytical method based on high-order orthogonal expansions using the Chebyshev polynomials of the first kind with the subsequent Fejér summation. The method is intended for the processing of regularly spaced DEMs within a single framework including DEM global approximation, denoising, generalization, as well as calculating the partial derivatives of elevation and local morphometric variables.

The method is exemplified by a portion of the Great Rift Valley and central Kenyan highlands. A DEM of this territory (the matrix 480 × 481 with a grid spacing of 30″) was extracted from the global DEM SRTM30_PLUS. We evaluated various sets of expansion coefficients (up to 7000) to approximate and reconstruct DEMs with and without the Fejér summation. Digital models of horizontal and vertical curvatures were computed using the first and second partial derivatives of elevation derived from the reconstructed DEMs. To evaluate the approximation accuracy, digital models of residuals (differences between the reconstructed DEMs and the initial one) were calculated. The test results demonstrated that the method is characterized by a good performance (i.e., a distinct monotonic convergence of the approximation) and a high speed of data processing. The method can become an effective alternative to common techniques of DEM processing.  相似文献   

福建前汛期区域暴雨客观预报模型研究   总被引：5，自引：4，他引：1       下载免费PDF全文

刘爱鸣 潘宁邹燕  张明席 《应用气象学报》2003,14(4):419-429

利用滑动分区切比雪夫展开方法,求取高度场特征分布的展开系数及其时间变量,通过相关分析,从中提取物理意义明确和相关性好的预报因子集和消空因子集,再通过预报因子的多形态组合分析,提炼出物理图像清晰的福建省前汛期区域暴雨预报模型。研究结果表明:以高度场的滑动分区切比雪夫展开系数做为研制前汛期的区域性暴雨预报模型的信息源是合理且可行的。切比雪夫正交多项式能够对要素场的内在特征信息进行定量化提取,生成彼此相互独立的场量因子;滑动分区展开技术可对场信息做极限化的开发,产生多种尺度的特征信息,从而获得对预报对象成因更完备的认识。  相似文献