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- Author: I Gohberg
- Publisher: Birkhäuser
- Year: 2014
- Pages: 247
- ISBN-10: 3034854714
- ISBN-13: 9783034854719
- Format: 17 x 24.4 x 1.4 cm, softcover
- Language: English
- SAVE -10% with code: EXTRA
Topics in Interpolation Theory of Rational Matrix-Valued Functions (e-book) (used book) | bookbook.eu
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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.
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- Author: I Gohberg
- Publisher: Birkhäuser
- Year: 2014
- Pages: 247
- ISBN-10: 3034854714
- ISBN-13: 9783034854719
- Format: 17 x 24.4 x 1.4 cm, softcover
- Language: English English
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.
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