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An explicit univariate and radical parametrization of the septic proper Zolotarev polynomials in power form [article]

Heinz-Joachim Rack, Robert Vajda
2020 arXiv   pre-print
The problem of determining an explicit one-parameter power form representation of the proper n-th degree Zolotarev polynomials on [-1,1] can be traced back to P. L. Chebyshev.  ...  The parametrization for the degrees n∈{2,3,4} is a rational one, whereas for n∈{5,6,7} it is a radical one.  ...  This contributes to the solution of ZFP which is one of E. Kaltofen's favorite open problems in symbolic computation [13, Section 2] .  ... 
arXiv:2002.00503v1 fatcat:boy7mxsjzrc2hcefcrb3bit4b4

Challenges of Symbolic Computation: My Favorite Open Problems

Erich Kaltofen
2000 Journal of symbolic computation  
The research challenges in symbolic computation at the close of the 20th century are formidable. I state my favorite eight open problems in symbolic computation. They range  ...  Open Problem 2 (Zolotarev's problem by Collins 1992) Eliminate the quantifiers and solve for n 6 on a computer: for r 0: min B=b 0 ++b n,2 x n,2 max ,1x1 jx n + rx n,1 ,Bxj The best approximation of a  ...  Open Problem 5 Compute Gröbner bases approximately by iterative methods for solving systems, such as Gauss-Seidel, conjugate gradient, Newton,...  ... 
doi:10.1006/jsco.2000.0370 fatcat:46vy6vmihrdgpirlmam4xaqgxm