Matrix-valued nevanlinna-pick interpolation with complexity constraint: an optimization approach
نویسندگان
چکیده
منابع مشابه
Matrix-valued Nevanlinna-Pick interpolation with complexity constraint: an optimization approach
Over the last several years a new theory of Nevanlinna-Pick interpolation with complexity constraint has been developed for scalar interpolants. In this paper we generalize this theory to the matrix-valued case, also allowing for multiple interpolation points. We parameterize a class of interpolants consisting of “most interpolants” of no higher degree than the central solution in terms of spec...
متن کاملA Constrained Nevanlinna-pick Interpolation Problem for Matrix-valued Functions
Recent results of Davidson-Paulsen-Raghupathi-Singh give necessary and sufficient conditions for the existence of a solution to the NevanlinnaPick interpolation problem on the unit disk with the additional restriction that the interpolant should have the value of its derivative at the origin equal to zero. This concrete mild generalization of the classical problem is prototypical of a number of...
متن کاملA Fast Algorithm for Matrix-Valued Nevanlinna-Pick Interpolation
In this paper, we derive a new fast algorithm for the matrixvalued Nevanlinna-Pick interpolation. Given n distinct points zi in the unit disk jzj < 1 and n complex matrices Wk of dimension m m, satisfying the Pick condition for 1 k n, the new Nevanlinna-Pick interpolation algorithm requires only 20 3 nm 3 complex arithmetic operations to evaluate the matrix-valued interpolatory rational functio...
متن کاملNevanlinna - Pick Interpolation For
We study the Nevanlinna-Pick problem for a class of subalgebras of H∞. This class includes algebras of analytic functions on embedded disks, the algebras of finite codimension in H∞ and the algebra of bounded analytic functions on a multiply connected domain. Our approach uses a distance formula that generalizes Sarason’s [18] work. We also investigate the difference between scalar-valued and m...
متن کاملMultivariable Operator-valued Nevanlinna-pick Interpolation: a Survey
The theory of Nevanlinna-Pick and Carathéodory-Fejér interpolation for matrixand operator-valued Schur class functions on the unit disk is now well established. Recent work has produced extensions of the theory to a variety of multivariable settings, including the ball and the polydisk (both commutative and noncommutative versions), as well as a time-varying analogue. Largely independent of thi...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: IEEE Transactions on Automatic Control
سال: 2003
ISSN: 0018-9286
DOI: 10.1109/tac.2003.820227