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Research

# Ph.D. Theses

## Efficient Algorithms for Computing the Nearest Polynomial with Constrained Roots

By Markus A. Hitz
The location of polynomial roots is sensitive to perturbations of the coefficients. Continuous changes of the coefficients of a polynomial move the roots continuously. We consider the problem of finding the minimal perturbations to the coefficients to move one or several roots to given loci. We measure minimality in the Euclidean distance to the coefficient vector, as well as the maximal coefficient-wise change in absolute value (infinity norm), and in the Manhattan norm ($l^1$-norm). In the Euclidean norm the computational task reduces to a least squares problem, in the infinity norm and the $l^1$-norm it can be formulated as a linear program.