Abstract
For a real univariate polynomial f and a closed domain D ⊂ C whose boundary C is represented by a piecewise rational function, we provide a rigorous method for finding a real univariate polynomial f ̃ such that f ̃ has a zero in D and ‖ f − f ̃ ‖ ∞ is minimal. First, we prove that if a nearest polynomial exists, there is a nearest polynomial f ̃ such that the absolute value of every coefficient of f − f ̃ is ‖ f − f ̃ ‖ ∞ with at most one exception. Using this property and the representation of C , we reduce the problem to solving systems of algebraic equations, each of which consists of two equations with two variables.
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