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 复样条
 complex spline
 ASYMPTOTIC EXPANSIONS FOR COMPLEX SPLINE AND (REAL) POLYNOMIAL SPLINE OF DEGREE EVEN 复样条及偶次(实)多项式样条的渐近展开 短句来源 Proofs of complex spline theorems 复样条几个定理的证明 短句来源 On Estimation of Cubic Complex Spline Approximation Orders for Singular Integrals 关于奇异积分三次复样条近似的误差阶估计 短句来源 It is known that a complex function (harmonic or analytic) can be approximated by complex spline functions in an efficient way which may be characterized by its simplicity and high accusacy. 我们知道复样条函数能以简单的方武以及很高的精度去逼近一个复函数。 短句来源
 “复样条”译为未确定词的双语例句
 The Progreso of Complex Splines 复样条函数的进展 短句来源 COMPLEX SPLINES AND APPROXIMATE SOLUTION FOR RIEMANN BOUNDARY PROBLEMS 复样条与Riemann边值问题的近似解 短句来源 In this paper, complex lacunary interpolation splines of C~2-class are discussed. 本文讨论了定义在单位圆上、具有均匀分布节点的s次(s≥3)C~2类复的缺插值样条函数。 对这一类复样条,解决了插值问题(存在性、唯一性),讨论了误差估计,并给出了一种渐近展开式。 短句来源
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 The Progreso of Complex Splines 复样条函数的进展 短句来源 Proofs of complex spline theorems 复样条几个定理的证明 短句来源 Complex Numbers 复数 短句来源 L spline function L样条函数 短句来源 Spline Wavelets 样条小波 短句来源

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 It is known that a complex function (harmonic or analytic) can be approximated by complex spline functions in an efficient way which may be characterized by its simplicity and high accusacy. It is simple, since it may be expressed by elementary functions; and is of high accuracy because the spline functions hold flexible Fitting property.The basis of the arguments may be referred to [15], [22], [24].Complex spline may be constructed from piece-wise complex polynomials defined on the boundary of the domain.The... It is known that a complex function (harmonic or analytic) can be approximated by complex spline functions in an efficient way which may be characterized by its simplicity and high accusacy. It is simple, since it may be expressed by elementary functions; and is of high accuracy because the spline functions hold flexible Fitting property.The basis of the arguments may be referred to [15], [22], [24].Complex spline may be constructed from piece-wise complex polynomials defined on the boundary of the domain.The piece-wise polgnomials may be the interpolatory or quasi-interpolatory, functions. As for the existence and the construction of these functions, one may refer to [24], [16].At the end of this paper, some open problems are presented. 我们知道复样条函数能以简单的方武以及很高的精度去逼近一个复函数。说它简单,是因为它可以由初等函数来表示;说它能达到很高的精度,是由于样条函数具有十分好的逼近性质,关于这些论点的依据.可参见[15]、[22]、[23]。复样条函数的特点是它在边界上由分段多项式构成,这种边界函数对被逼近的函数可以是插值的或拟插值的,关于这方面的介绍可见[24]及[16]。另一方面,复样条函数能构造出单位圆上的解析函数的正交基组(见[1]—[7])。本文最后介绍一些有待进一步探讨的问题。 In this paper, complex lacunary interpolation splines of C~2-class are discussed. Theorems are established concerning the existence, uniqueness and estimate for the rate of convergence. These are generalizations of the results on the real splines of the same type as was discussed in Chen Tianping's article "On Lacunary Interpolation Splines" (cf. [1]). 本文讨论了定义在单位圆上、具有均匀分布节点的s次(s≥3)C~2类复的缺插值样条函数。对这一类复样条,解决了插值问题(存在性、唯一性),讨论了误差估计,并给出了一种渐近展开式。实的缺插值样条问题的讨论已经很多。在[1]中,陈天平讨论了一种C~2类的缺插值样条函数,其处理方法能避免许多冗繁的计算。本文可看作[1]在复情形下的推广。相对于实样条而言,复样条的研究虽然早已开展,但国内外这方面的工作还不多(见文献[3]～[5]),也未见专门讨论缺插值复样条的文章。一般来说,复样条研究比较困难,即使对单位圆上均匀节点高次复样条的插值问题讨论,也是相当烦琐的(见[3])。但是对于本文所研究的这种复样条来说,却能较方便地用与[1]中类似的方法来讨论,并得到了比较完善的结果,而且可以看到,[2]中的结果也可能移植到我们这里来。 This paper discusses the estimation of approximation orders of singular integrals over a general curve by means of cubic complex spline. For some classes of functions the orders are given and meanwhile. 讨论曲线上柯西型奇异积分利用三次复样条进行近似计算的误差估计,对于相关函数类给出了这类逼近的误差阶.
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