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基于Thiele型连分式构造求积公式,这类求积公式能再生由Thiele型连分式前三项渐近式的线性组合所表示的任意有理函数,接着算出求积余项,并推导出分母在给定区间上无零点的充分条件.更进一步,通过等分给定区间,构造相应的复化求积公式,并算出求积余项.研究表明,在若干条件满足的前提下,复化求积公式序列能一致收敛于积分真值,一些数值算例说明了这一点. 相似文献
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首先利用Newton-Pade表中部分序列推导出连分式,提出逆差商算法,算出关于高阶导数与高阶差商的连分式插值余项.接着,构造基于此类连分式的有理求积公式与相应的复化求积公式,算出相应的求积余项,研究表明,在一定条件下,求积公式序列一致收敛于积分真值.然后,为保证连分式计算顺利进行,研究连分式分母非0的充分条件.最后,若干数值算例表明,对某些函数采用新提出的复化有理求积公式计算数值积分,所得结果优于采用Simpson公式. 相似文献
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在本文中,我们以二元三次复插值样条函数作为逼近工具,给出了光滑封闭曲线上的核密度中含有参数的各种Cauchy主值积分的求积公式,误差估计及逼近性定理。 相似文献
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开口曲线上的奇异积分近似求积公式 总被引:1,自引:1,他引:0
徐红岭 《数学的实践与认识》2003,33(8):142-144
本文利用复插值样函数讨论了开口光滑曲线上的奇异积分在被积函数分别属于 H类和 H* 类时的近似求积公式 ,给出了误差估计和收敛性 相似文献
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针对经典NGM(1,1,k)在背景值的影响下模型精度(拟合精度与预测精度)不高这一现状,结合复化求积公式中的复化梯形公式,推导了一种新的背景值优化公式.通过7类测试数据和2类实际数据的验证表明:推导的NGM(1,1,k)背景值优化公式显著地提高了NGM(1,1,k)的模型精度和实用性. 相似文献
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通过分析基本数值求积公式的双侧逼近现象,利用加权平均的方法构造出了比原来求积公式至少高二次代数精度新的混合型求积公式,使得积分近似值精度得到大幅度提高,并给出应用它们求数值积分的具体实例. 相似文献
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构建了一类二维带边界偏导数值的复化数值积分公式,给出了所建立的两种数值积分公式的稳定性分析、误差分析和代数精度.与二维复化四点高斯数值积分公式相对比,所建立的带边界偏导数值的复化梯形、复化辛普森求积公式在达到相同精度时所需积分节点大大减少,积分的时间复杂度也随之大大减少,实例验证结果良好. 相似文献
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Cotes数值求积公式的校正 总被引:2,自引:0,他引:2
本文研究了Cotes数值求积公式代数精度的问题,给出了Cotes求积公式余项"中间点"的渐进性定理.利用该定理得到了改进的Cotes求积公式,并证明了改进后的Cotes求积公式比原来的公式具有较高的代数精度. 相似文献
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本文研究一类线性随机延迟积分微分方程Euler-Maruyama方法的MS-稳定性.首先,我们讨论方程真解的均方指数稳定性条件.然后,在此假设条件下,证明了带有复合梯形公式的Euler-Maruyama方法是MS-稳定的.最后,数值试验验证了本文的结论. 相似文献
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Akalu Tefera Aklilu Zeleke 《International Journal of Mathematical Education in Science & Technology》2013,44(8):1091-1096
In this note we present a class of functions (f, g) that satisfy ‘freshman rules’ in calculus. 相似文献
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A yield condition is obtained for circular cylindrical shells made of a definite class of fiber-reinforced composite material
whose components possess plastic properties. It is shown that, in the plane of generalized stresses — the axial bending moment
and the circumferential force (when the axial force is absent) — the yield curve consists of two linear and four curvilinear
sections. By approximating the curvilinear sections, we get a piecewise linear yield condition described by a hexagon in the
plane indicated. The nonlinear equations and the corresponding piecewise linear equations of the yield condition for particular
cases are given in the form of tables. In solving specific boundary-value problems, we consider a circular cylindrical shell
simply supported at its ends and loaded with a uniform internal pressure, for which the load-carrying capacity is determined
in relation to the mechanical properties of composite components and some characteristic geometrical parameters. The results
of numerical calculations are represented in the form of graphs.
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Translated from Mekhanika Kompozitnykh Materialov, Vol. 42, No. 5, pp. 655–666, September–October, 2006. 相似文献
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The load-carrying capacity of circular plates made of a fiber-reinforced composite and loaded with axisymmetric transverse forces under axisymmetric boundary conditions is investigated. The plates can be freely supported or clamped along their contour. To the known yield condition used, in the plane of main bending moments, there correspond irregular hexagons, which depend on the mechanical properties of composite constituents and some characteristic geometrical parameters. It is shown that, depending on the ratio of ultimate radial and circumferential bending moments, in the plastic state, the circular plates (the central part of the clamped plates) take the form of a cone or a frustum of cone. For each of the cases, the limit load is found, which is a function of the above-mentioned mechanical parameters. The statically allowable fields of bending moments and the corresponding allowable fields of deflection rates are determined. The solutions found are exact. Special cases for the freely supported plates are analyzed, and the results obtained are presented in the form of graphs.__________Translated from Mekhanika Kompozitnykh Materialov, Vol. 41, No. 2, pp. 177–192, March–April, 2005. 相似文献
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Edward W. Packel 《Mathematical Social Sciences》1980,1(1):93-100
Let F a two-alternative voting rule and GF the subgroup of permutations of the voters under which F is invariant. Group theoretic properties of GF provide information about the voting rule F. In particular, sets of imprimitivity of GF describe the ‘committee decomposition’ structure of F and permutation group transitivity of GF (equipotency) is shown to be closely connected with equal distribution of power among the voters. If equipotency replaces anonymity in the hypotheses of May's theorem, voting rules other than simple majority are possible. By combining equipotency with two additional social choice conditions a new characterization of simple majority rule is obtained. Equipotency is proposed as an important alternative to the more restrictive anonymity as a fairness criterion in social choice. 相似文献
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In this paper, locally Lipschitz functions acting between infinite dimensional normed spaces are considered. When the range
is a dual space and satisfies the Radon–Nikodym property, Clarke’s generalized Jacobian will be extended to this setting.
Characterization and fundamental properties of the extended generalized Jacobian are established including the nonemptiness,
the β-compactness, the β-upper semicontinuity, and a mean-value theorem. A connection with known notions is provided and chain rules are proved using
key results developed. This included the vectorization and restriction theorem, and the extension theorem. Therefore, the
generalized Jacobian introduced in this paper is proved to enjoy all the properties required of a derivative like-set.
Research of the first author is supported by the Hungarian Scientific Research Fund (OKTA) under grant K62316.
Research of the second author is supported by the National Science Foundation under grant DMS-0306260. 相似文献
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Jingcheng Tong Peter A. Braza 《International Journal of Mathematical Education in Science & Technology》2013,44(2):277-279
We derive two simple and memorizable formulas for the radius of convergence of a power series which seem to be appropriate for teaching in an introductory calculus course. 相似文献
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Ping-Qi Pan 《Operations Research Letters》2008,36(3):309-313
We report a remarkable success of nested pricing rules over major pivot rules commonly used in practice, such as Dantzig’s original rule as well as the steepest-edge rule and Devex rule. 相似文献