APPROXIMATION AND INTERPOLATION BY VECTOR VALUE CONTINUED FACTIONS
向量连分式逼近与插值

It is shown tbat the Samelson nverse may be used to construct vector valuedcontinued fraction expansions. An efficient algorithm of the expansion coefficientsis established. As an application, the well-known Thiele theorem is generalized tothe vector case. Furthermore the Continurd fraction approximation of vector valuedfunctions is introduced, and its rationalness, characteriration, uniqueness and remainder term are given. Finally, vector osculatory interpolation by continued fractionsis proposed and discussed.