内积空间上向量值Padé-型逼近表的块状结构特征

Block Structure of Vector-Valued Padé-Type Table in the Inner Space

从多项式空间到向量空间引入一种广义线性泛函,在内积空间上定义和构造向量值Padé-型逼近.借助向量值Padé-型逼近的误差公式,给出关于线性泛函的正交多项式的定义,同时推导出向量值Padé-型逼近表的块状结构特征.利用Padé-型逼近表的这一特征,可以减少向量值Padé-型逼近的计算量.最后,通过数值实例说明该方法的有效性.

A vector-valued Padé-type approximation is defined in the inner space by introducing a generalized linear functional from a polynomial space to a vector space.With the error formula for vector-valued Padé-type approximation,the orthogonal polynomial with respect to a generalized linear functional is defined.The block structure of Padé-type table is derived.The structure can be used to reduce computation of Padé-type approximations.An example is given to illustrate effectiveness of the method.