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1998
Springer

Efficient Algorithms for Computing the Nearest Polynomial with Constrained Roots

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Efficient Algorithms for Computing the Nearest Polynomial with Constrained Roots
Continuous changes of the coefficients of a polynomial move the roots continuously. We consider the problem finding the minimal perturbations to the coefficients to move a root to a given locus, such as a single point, the real or imaginary axis, the unit circle, or the right half plane. We measure minimality in both the Euclidean distance to the coefficient vector and maximal coefficient-wise change in absolute value (infinity norm), either with entirely real or with complex coefficients. If the locus is a piecewise parametric curve, we can give efficient, i.e., polynomial time algorithms for the Euclidean norm; for the infinity norm we present an efficient algorithm when a root of the minimally perturbed polynomial is constrained to a single point. In terms of robust control, we are able to compute the radius of stability in the Euclidean norm for a wide range of convex open domains of the complex plane.
Markus A. Hitz, Erich Kaltofen
Added 06 Aug 2010
Updated 06 Aug 2010
Type Conference
Year 1998
Where ISSAC
Authors Markus A. Hitz, Erich Kaltofen
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