Root neighborhoods of a polynomial
Mathematics of Computation
Real and complex analysis, 3rd ed.
Real and complex analysis, 3rd ed.
Efficient algorithms for computing the nearest polynomial with constrained roots
ISSAC '98 Proceedings of the 1998 international symposium on Symbolic and algebraic computation
Efficient algorithms for computing the nearest polynomial with a real root and related problems
ISSAC '99 Proceedings of the 1999 international symposium on Symbolic and algebraic computation
The nearest polynomial with a given zero, and similar problems
ACM SIGSAM Bulletin
Robust Control: The Parametric Approach
Robust Control: The Parametric Approach
The nearest polynomial with a given zero, revisited
ACM SIGSAM Bulletin
Locating real multiple zeros of a real interval polynomial
Proceedings of the 2006 international symposium on Symbolic and algebraic computation
The nearest polynomial with a zero in a given domain from a geometrical viewpoint
Proceedings of the twenty-first international symposium on Symbolic and algebraic computation
The Nearest Real Polynomial with a Real Multiple Zero in a Given Real Interval
Computer Mathematics
The nearest polynomial with a zero in a given domain
Theoretical Computer Science
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For a real univariate polynomial f and a bounded closed domain D ⊂ C whose boundary C is a simple closed curve of finite length and is represented by a piecewise rational function, we provide a rigorous method for finding the real univariate polynomial f such that f has a zero in D and ||f -- f||∞ is minimal. First, we prove 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. Furthermore, every equation is of degree one with respect to one of the two variables.