向量连分式逼近与插值

§！.向量连分式展开式 给定不同实数组成的序列∏_x~∞={x_0,x_1,x_2,…}和由对应的有限向量组成的序列?_z~∞={V~((0)),V~((1)),V~((2)),…},其中V~((i))=V(x_i),V~((i))∈C~d.向量的Samelson逆变换定义为 V~(-1)(x)=V~*(x)/|V(x)|~2,V~*是V的共轭向量.(1) 定义1.?_lx_0x_1…x_l]称为V(x)的第l阶反差商,其中

APPROXIMATION AND INTERPOLATION BY VECTOR VALUE CONTINUED FACTIONS

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.