One of the basic interpolation problems from our point of view is the problem of building a scalar rational function if its poles and zeros with their multiplicities are given. If one assurnes that the function does not have a pole or a zero at infinity, the formula which solves this problem is (1) where Zl , " " Z/ are the given zeros with given multiplicates nl, " " n / and Wb" " W are the given p poles with given multiplicities ml, . . . , m , and a is an arbitrary nonzero number. p An obvious necessary and sufficient condition for solvability of this simplest Interpolation pr- lern is that Zj :f: wk(1~ j ~ 1, 1~ k~ p) and nl +. . . +n/ = ml +. . . +m ‘ p The second problem of interpolation in which we are interested is to build a rational matrix function via its zeros which on the imaginary line has modulus 1. In the case the function is scalar, the formula which solves this problem is a Blaschke product, namely z z. )mi n u(z) = all = l~ (2) J ( Z+ Zj where [o] = 1, and the zj’s are the given zeros with given multiplicities mj. Here the necessary and sufficient condition for existence of such u(z) is that zp :f: – Zq for 1~ ]1, q~ n.
€57.77
购买此电子书可免费获赠一本！
语言 英语 ● 格式 PDF ● ISBN 9783034854696 ● 出版者 Birkhauser Basel ● 发布时间 2013 ● 下载 3 时 ● 货币 EUR ● ID 6289819 ● 复制保护 Adobe DRM
需要具备DRM功能的电子书阅读器
来自同一作者的更多电子书 / 编辑
87,073 此类电子书
