The singular value decomposition for polynomial systems
ISSAC '95 Proceedings of the 1995 international symposium on Symbolic and algebraic computation
Efficient algorithms for computing the nearest polynomial with constrained roots
ISSAC '98 Proceedings of the 1998 international symposium on Symbolic and algebraic computation
On approximate GCDs of univariate polynomials
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
Approximate polynomial Gcds, Padé approximation, polynomial zeros and bipartite graphs
Proceedings of the ninth annual ACM-SIAM symposium on Discrete algorithms
The nearest polynomial with a given zero, and similar problems
ACM SIGSAM Bulletin
The nearest polynomial with a zero in a given domain
Proceedings of the 2007 international workshop on Symbolic-numeric computation
The nearest polynomial of lower degree
Proceedings of the 2007 international workshop on Symbolic-numeric computation
On real factors of real interval polynomials
Proceedings of the 2007 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
On real factors of real interval polynomials
Journal of Symbolic Computation
Proceedings of the 2010 International Symposium on Symbolic and Algebraic Computation
Rounding coefficients and artificially underflowing terms in non-numeric expressions
ACM Communications in Computer Algebra
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
Using weighted norms to find nearest polynomials satisfying linear constraints
Proceedings of the 2011 International Workshop on Symbolic-Numeric Computation
Computing the nearest singular univariate polynomials with given root multiplicities
Theoretical Computer Science
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In his 1999 SIGSAM BULLETIN paper [7], H. J. Stetter gave an explicit formula for finding the nearest polynomial with a given zero. This present paper revisits the issue, correcting a minor omission from Stetter's formula and explicitly extending the results to different polynomial bases.Experiments with our implementation demonstrate that the formula may not after all, fully solve the problem, and we discuss some outstanding issues: first, that the nearest polynomial with the given zero may be identically zero (which might be surprising), and, second, that the problem of finding the nearest polynomial of the same degree with a given zero may not, in fact, have a solution. A third variant of the problem, namely to find the nearest monic polynomial (given a monic polynomial initially) with a given zero, a problem that makes sense in some polynomial bases but not others, can also be solved with Stetter's formula, and this may be more satisfactory in some circumstances. This last can be generalized to the case where some coefficients are intrinsic and not to be changed, whereas others are empiric and may safely be changed. Of course, this minor generalization is implicit in [7]; This paper simply makes it explicit.