| 构造矩阵有理插值函数的方法 |
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| 引用本文： | 朱功勤.构造矩阵有理插值函数的方法[J].合肥工业大学学报(自然科学版),2005,28(9):1200-1203. |
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| 作者姓名： | 朱功勤 |
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| 作者单位： | 合肥工业大学,理学院,安徽,合肥,230009 |
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| 基金项目： | 国家自然科学基金资助项目(10171026) |
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| 摘 要： | 熟知的构造矩阵值有理插值函数的方法,是基于矩阵的古典逆或Samelson逆,利用连分式给出的,其算法可行性不易预知。借助构造向量值有理插值的方法,引入多个参数,定义一对多项式:代数多项式和矩阵值多项式,并利用两多项式相等的充分必要条件,通过求解方程组确定参数,并由此给出类似于多项式插值的矩阵值有理插值公式;该公式简单,便于实际应用。
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| 关 键 词： | 矩阵值 有理插值 参数 方程组 |
| 文章编号： | 1003-5060(2005)09-1200-04 |
| 修稿时间： | 2005年6月27日 |
Method of constructing matrix-valued rational interpolation functions |
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| ZHU Gong-qin.Method of constructing matrix-valued rational interpolation functions[J].Journal of Hefei University of Technology(Natural Science),2005,28(9):1200-1203. |
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| Authors: | ZHU Gong-qin |
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| Abstract: | The well-known algorithms of constructing matrix-valued rational interpolations are based on classical or Samelson inverse and continued fractions,and their applicability is not easily forecast.In light of the vector-valued rational interpolation method,multi-parameters are introduced herein and a group of polynomials,that is,an algebraic polynomial and matrix-valued polynomials,are defined.By using the necessary and sufficient conditions for polynomials identity,equations are solved to determine those parameters,and the formula of the matrix-valued rational interpolation similar to Lagrange polynomial interpolation is given.The formula is simple,flexible and more applicable. |
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| Keywords: | matrix-valued rational interpolation parameter system of equations |
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