Abstract:

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.

Key words: vector-valued; Padé-type approximation; orthogonal polynomial; block structure