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
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
Efficient algorithms for computing the nearest polynomial with constrained roots
Efficient algorithms for computing the nearest polynomial with constrained roots
Numerical Polynomial Algebra
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
On real factors of real interval polynomials
Journal of Symbolic Computation
Computing the nearest polynomial with a zero in a given domain by using piecewise rational functions
Journal of Symbolic Computation
The nearest complex polynomial with a zero in a given complex domain
Theoretical Computer Science
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In this paper, we consider the problem of a nearest polynomial with a given root in the complex field (the coefficients of the polynomial and the root are complex numbers). We are interested in the existence and the uniqueness of such polynomials. Then we study the problem in the real case (the coefficients of the polynomial and the root are real numbers), and in the real-complex case (the coefficients of the polynomial are real numbers and the root is a complex number). We derive new formulas for computing such polynomials.