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To solve Fredholm integral equations of the second kind, a generalized linear functional is introduced and a new function-valued Pade-type approximation is denned. By means of the power series expansion of the solution, this method can construct an approximate solution to solve the given integral equation. On the basis of the orthogonal polynomials, two useful determinant expressions of the numerator polynomial and the denominator polynomial for Pade-type approximation are explicitly given. 相似文献
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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. 相似文献
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关于广义逆的向量连分式插值样条 总被引:2,自引:1,他引:1
本文首次引入了关于广义逆的向量有理插值样条的概念.这类插值样条具有Thiele型连分式的截断分式的表现形式.在它的构造过程中,不必用到连分式的三项递推关系,本文得到的新的有效的系数算法具有递推运算的特点.存在性的一个充分条件得以建立.包括唯一性在内的有关插值问题的某些结果得到证明.最后,本文给出了一个精确的插值误差公式. 相似文献
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对多输入多输出大规模动力系统的模型简化提出了一种新的方法.它是一种投影方法,其投影依赖于奇异值分解(singular value decomposition,SVD)和Krylov子空间.该方法实际上等价于求解一个Frobenius范数最小二乘问题.通过该方法降阶后的模型能准确地匹配原模型的前r个模,剩余的高阶模以Frobenius范数最小二乘法的形式逼近原模型的模,其中,r是降阶系统的维数.还将该方法推广到任意插值点的模匹配,数值例子也证明了该方法的有效性. 相似文献
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引用两种加速计算PageRank的算法,分别为内外迭代法和多分裂迭代算法.从这两种方法中,得到改进的多分裂迭代方法.首先,详细介绍了算法实施过程.然后,对此算法的收敛性进行证明,并且将此算法的谱半径与原有的多分裂迭代算法的谱半径进行比较.最后,数值实验说明我们的算法的计算速度比原有的多分裂迭代法要快. 相似文献
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矩阵有理插值及其误差公式 总被引:24,自引:1,他引:24
矩阵有理插值及其误差公式顾传青,陈之兵(合肥工业大学)MATRIXVALUEDRATIONALINTERPOLANTSANDITSERRORFORMULA¥GuChuan-qing;ChenZhi-bing(HefeiUniversityofTech... 相似文献
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