EXISTENCE AND UNIQUENESS OF SOLUTIONS FOR NONLINEAR BOUNDARY VALUE PROBLEMS OF VOLTERRA－HAMMERSTEIN TYPE INTEGRODIFFERENTIAL EQUATION

ＥＸＩＳＴＥＮＣＥＡＮＤＵＮＩＱＵＥＮＥＳＳＯＦＳＯＬＵＴＩＯＮＳＦＯＲＮＯＮＬＩＮＥＡＲＢＯＵＮＤＡＲＹＶＡＬＵＥＰＲＯＢＬＥＭＳＯＦＶＯＬＴＥＲＲＡ－ＨＡＭＭＥＲＳＴＥＩＮＴＹＰＥＩＮＴＥＧＲＯＤＩＦＦＥＲＥＮＴＩＡＬＥＱＵＡＴＩＯＮ￥ＷａｎｇＧ...     

广义Chebyshev－Vandermonde方程组的快速算法与求逆公式

广义Ｃｈｅｂｙｓｈｅｖ－Ｖａｎｄｅｒｍｏｎｄｅ方程组的快速算法与求逆公式成礼智（国防科技大学）ＩＮＥＲＳＩＯＮＦＯＲＭＵＬＡＡＮＤＦＡＳＴＳＯＬＵＴＩＯＮＦＯＲＧＥＮＥＲＡＬＣＨＥＢＹＳＨＥＶ－ＶＡＮＤＥＲＭＯＮＤＥＥＱＵＡＴＩＯＮＳ￥ＣｈｅｎｇＬｉ...     

POSITIVE SOLUTIONS AND BIFURCATION OF FULLY NONLINEAR ELLIPTIC EQUATIONS INVOLVING SUPER－CRITICAL SOBOLEV EXPONENTS

ＰＯＳＩＴＩＶＥＳＯＬＵＴＩＯＮＳＡＮＤＢＩＦＵＲＣＡＴＩＯＮＯＦＦＵＬＬＹＮＯＮＬＩＮＥＡＲＥＬＬＩＰＴＩＣＥＱＵＡＴＩＯＮＳＩＮＶＯＬＶＩＮＧＳＵＰＥＲ－ＣＲＩＴＩＣＡＬＳＯＢＯＬＥＶＥＸＰＯＮＥＮＴＳ￥ＱＵＣＨＡＮＧＺＨＥＮＧ（屈长征）（Ｉｎｓ...     

A CLASS OF SINGULAR PERTURBATIONS FOR SECOND ORDER QUASI－LINEAR BOUNDARY VALUE PROBLEMS ON INFINITE INTERVAL

ＡＣＬＡＳＳＯＦＳＩＮＧＵＬＡＲＰＥＲＴＵＲＢＡＴＩＯＮＳＦＯＲＳＥＣＯＮＤＯＲＤＥＲＱＵＡＳＩ－ＬＩＮＥＡＲＢＯＵＮＤＡＲＹＶＡＬＵＥＰＲＯＢＬＥＭＳＯＮＩＮＦＩＮＩＴＥＩＮＴＥＲＶＡＬＺＨＡＯＷＥＩＬＩ（赵为礼）（ＤｅｐａｒｔｍｅｎｔｏｆＭａｔｈ...     

ELLIPTIC H~2－VOLTERRA PROJECTION AND THE H~1－GALERKIN METHODS FOR THE INTEGRO－DIFFERENTIAL EQUATIONS OF EVOLUTION

ＥＬＬＩＰＴＩＣＨ~２－ＶＯＬＴＥＲＲＡＰＲＯＪＥＣＴＩＯＮＡＮＤＴＨＥＨ~１－ＧＡＬＥＲＫＩＮＭＥＴＨＯＤＳＦＯＲＴＨＥＩＮＴＥＧＲＯ－ＤＩＦＦＥＲＥＮＴＩＡＬＥＱＵＡＴＩＯＮＳＯＦＥＶＯＬＵＴＩＯＮ￥ＳＵＮＰＥＮＧＴＡＯＡｂｓｔｒａｃｔ：Ｔｈｉｓｐ...     

UNIFORMLY VALID ASYMPTOTIC APPROXIMATIONS FOR NONLINEAR SINGULARLY－PERTURBED VECTOR BOUNDARY VALUE PROBLEMS

ＵＮＩＦＯＲＭＬＹＶＡＬＩＤＡＳＹＭＰＴＯＴＩＣＡＰＰＲＯＸＩＭＡＴＩＯＮＳＦＯＲＮＯＮＬＩＮＥＡＲＳＩＮＧＵＬＡＲＬＹ－ＰＥＲＴＵＲＢＥＤＶＥＣＴＯＲＢＯＵＮＤＡＲＹＶＡＬＵＥＰＲＯＢＬＥＭＳ￥ＳｈｉＹｕｍｉｎｇ（ＱｕｆｕＮｏｒｍａｌＵｎｉｖｅｒｓ...     

GLOBAL ATTRACTIVITY OF LINEAR NON－AUTONOMOUS NEUTRAL DIFFERENTIAL－DIFFERENCE EQUATIONS

ＧＬＯＢＡＬＡＴＴＲＡＣＴＩＶＩＴＹＯＦＬＩＮＥＡＲＮＯＮ－ＡＵＴＯＮＯＭＯＵＳＮＥＵＴＲＡＬＤＩＦＦＥＲＥＮＴＩＡＬ－ＤＩＦＦＥＲＥＮＣＥＥＱＵＡＴＩＯＮＳＨＥＸＵＥＺＨＯＮＧ（何学中）（ＤｅｐａｒｔｍｅｎｔｏｆＭａｔｈｅｍａｔｉｃｓ，Ｎｉｎｇｘｉ...     

EXISTENCE OF POSITIVE RADIAL SOLUTIONS AND ENTIRE SOLUTIONS FOR QUASILINEAR SINGULAR BOUNDARY VALUE PROBLEMS

ＥＸＩＳＴＥＮＣＥＯＦＰＯＳＩＴＩＶＥＲＡＤＩＡＬＳＯＬＵＴＩＯＮＳＡＮＤＥＮＴＩＲＥＳＯＬＵＴＩＯＮＳＦＯＲＱＵＡＳＩＬＩＮＥＡＲＳＩＮＧＵＬＡＲＢＯＵＮＤＡＲＹＶＡＬＵＥＰＲＯＢＬＥＭＳＹａｎｇＺｕｏｄｏｎｇ（杨作东）＆ＧｕｏＺｏｎｇｍｉｎｇ（郭...     

广义Chebyshev－Vandermonde方程组的快速算法与求逆公式

广义Ｃｈｅｂｙｓｈｅｖ－Ｖａｎｄｅｒｍｏｎｄｅ方程组的快速算法与求逆公式成礼智（国防科技大学）ＩＮＥＲＳＩＯＮＦＯＲＭＵＬＡＡＮＤＦＡＳＴＳＯＬＵＴＩＯＮＦＯＲＧＥＮＥＲＡＬＣＨＥＢＹＳＨＥＶ－ＶＡＮＤＥＲＭＯＮＤＥＥＱＵＡＴＩＯＮＳ￥ＣｈｅｎｇＬｉ...     

ON GLOBAL SOLUTION FOR A CLASS OF SYSTEMS OF MULTI－DIMENSIONAL GENERALIZED ZAKHAROV TYPE EQUATION

ＯＮＧＬＯＢＡＬＳＯＬＵＴＩＯＮＦＯＲＡＣＬＡＳＳＯＦＳＹＳＴＥＭＳＯＦＭＵＬＴＩ－ＤＩＭＥＮＳＩＯＮＡＬＧＥＮＥＲＡＬＩＺＥＤＺＡＫＨＡＲＯＶＴＹＰＥＥＱＵＡＴＩＯＮＧＵＯＢＯＬＩＮＧ（郭柏灵）（ＩｎｓｔｉｔｕｔｅｏｆＡｐｐｌｉｅｄａｎｄＣｏｍｐｕ...     

预给极点的向量有理插值及性质

1　引　　言在工程技术中经常会遇到一些多元奇异函数的计算问题,常规的有理插值方法无疑为这类问题的近似求解提供了有效的途径,但有时逼近效果不一定十分理想,其重要原因之一是人们往往采用统一的框架去构造有理插值公式,而忽略了被逼近对象的一些本质特征.针对某些具体问题,例如已知被逼近的向量值函数的奇异点的有关信息,构造一种预给极点的向量有理插值格式就显得很有必要,其逼近效果自然会更理想.设R2中的点集Πn,m={(xi,yj)|i=0,1,…,n;j=0,1,…,m},相应的d维向量集Vn,m={Vi,j∈Cd|i=0,1,…,n;j=0,1,…,m}.设V∈Cd为任一d维…     

二元Thile型向量有理插值的误差公式

借助于Ｓｏｍｅｌｓｏｎ广义逆，文［１］首次讨论了多元向量有理插值问题．本文得到了二元Ｔｈｉｅｌｅ型向量有理插值的一个精确的误差公式．     

MATRIX ALGORITHMS AND ERROR FORMULA FOR BIVARIATE THIELE-TYPE RECTANGULAR MATRIX VALUED RATIONAL INTERPOLATION

A new method for the construction of bivariate matrix valued rational interpolants (BGIRI) on a rectangular grid is presented in [6]. The rational interpolants are of Thiele-type continued fraction form with scalar denominator. The generalized inverse introduced by [3]is gen-eralized to rectangular matrix case in this paper. An exact error formula for interpolation is ob-tained, which is an extension in matrix form of bivariate scalar and vector valued rational interpola-tion discussed by Siemaszko[l2] and by Gu Chuangqing [7] respectively. By defining row and col-umn-transformation in the sense of the partial inverted differences for matrices, two type matrix algorithms are established to construct corresponding two different BGIRI, which hold for the vec-tor case and the scalar case.     

二元对角向量值有理插值的算法

首先提出了二元对角向量值有理插值问题,它包括主对角和副对角两种向量值有理插值,并分别给出了主对角线和副对角线上向量值有理插值的两种算法,即直接求系数bi,j的算法和基于Samelson广义逆所定义的特殊初等变换的矩阵算法.然后构造了在预给极点情况下求主对角线和副对角线上向量值有理插值的矩阵算法.最后给出多个数值例子说明上述算法的有效性.     

ALGORITHMS FOR LACUNARY VECTOR VALUED RATIONAL INTERPOLANTS

Efficient algorithms are established for the computation of bivariate lacunary vector valued rational interpolants based on the branched continued fractions and a numerical example is given to show how the algorithms are implemented,     

Bivariate composite vector valued rational interpolation

In this paper we point out that bivariate vector valued rational interpolants (BVRI) have much to do with the vector-grid to be interpolated. When a vector-grid is well-defined, one can directly design an algorithm to compute the BVRI. However, the algorithm no longer works if a vector-grid is ill-defined. Taking the policy of ``divide and conquer', we define a kind of bivariate composite vector valued rational interpolant and establish the corresponding algorithm. A numerical example shows our algorithm still works even if a vector-grid is ill-defined.

     

BIVARIATE RATIONAL INTERPOLANTS WITHRECTANGLE-HOLE-STRUCTURE

1.IntroductionGivenasetofdistinctrealpoints{xi,i~0,1,2,',n:xiER}andasetofcomplexvectordata{d'),i=0,1,2,',n:n)ECd},Graves-Momsshowed[5]thatthevectorvaluedThieletypecontinuedfractioncanservetointerpolatethegivenvectors.TheconstructionprocessiscloselyralatedtotheadoptionoftheSamelsoninverseforvectorswhere7denotesthecomplexconjugateofvector6.ItwasprovedthatS(x)isavectorvaluedrationalfunctionwithnumeratorbeingad-dimensionalpolynomialofdegreenanddenominatorbeingapolynomialofdegree2[n/2],here…     

NEVILLE-TYPE VECTOR VALUED RATIONAL INTERPOLANTS

A new kind of vector valued rational interpolants is established by means ofSamelson inverse, with scalar numerator and vector valued denominator. It is essen-tially different from that of Graves-Morris(1983), where the interpolants are constructedby Thiele-type continued fractions with vector valued numerator and scalar denomina-tor. The new approach is more suitable to calculate the value of a vector valued functionfor a .qiven point. And an error formula is also .qiven and proven.     

VECTOR VALUED RATIONAL INTERPOLANTS BY TRIPLE BRANCHED CONTINUED FRACTIONS

Triple branched continued fractions (TBCFs) are constructed by means of well-define Thiele-type partial inverted differences. The characterizatioon theorem, uniqueness theorem andsome projection identity properties are obtained for vector valued rational interpolants hy TBCFs.     

构造二元向量值有理插值函数的一种新方法

At present, the methods of constructing vector valued rational interpolation function in rectangular mesh are mainly presented by means of the branched continued fractions. In order to get vector valued rational interpolation function with lower degree and better approximation effect, the paper divides rectangular mesh into pieces by choosing nonnegative integer parameters d1 （0 〈 dl ≤ m） and d2 （0 ≤ d2≤ n）, builds bivariate polynomial vector interpolation for each piece, then combines with them properly. As compared with previous methods, the new method given by this paper is easy to compute and the degree for the interpolants is lower.