Root neighborhoods of a polynomial
Mathematics of Computation
Efficient algorithms for computing the nearest polynomial with constrained roots
ISSAC '98 Proceedings of the 1998 international symposium on Symbolic and algebraic computation
Journal of Symbolic Computation - Special issue on symbolic numeric algebra for polynomials
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
Optimization by Vector Space Methods
Optimization by Vector Space Methods
Robust Control: The Parametric Approach
Robust Control: The Parametric Approach
A note on a nearest polynomial with a given root
ACM SIGSAM Bulletin
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
Proceedings of the 2007 international workshop on Symbolic-numeric computation
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Given f茂戮驴 茂戮驴[x] and a closed real interval I, we provide a rigorous method for finding a nearest polynomial with a real multiple zero in I, that is, $\tilde{f}\in\mathbb{R}[x]$ such that $\tilde{f}$ has a multiple zero in Iand $\|f - \tilde{f}\|_\infty$, the infinity norm of the vector of coefficients of , is minimal. First, we prove that if a nearest polynomial exists, there is a nearest polynomial $\tilde{g}\in\mathbb{R}[x]$ such that the absolute value of every coefficient of $f-\tilde{g}$ is $\|f - \tilde{f}\|_\infty$ with at most one exceptional coefficient. Using this property, we construct h茂戮驴 茂戮驴[x] such that a zero of his a real multiple zero 茂戮驴茂戮驴 Iof $\tilde{g}$. Furthermore, we give a rational function whose value at 茂戮驴is $\|f - \tilde{f}\|_\infty$.