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Solving a polynomial equation: Some history and recent progress. (English) Zbl 0873.65050

Summary: The classical problem of solving an \(n\)th degree polynomial equation has substantially influenced the development of mathematics throughout the centuries and still has several important applications to the theory and practice of present-day computing. We briefly recall the history of the algorithmic approach to this problem and then review some successful solution algorithms. We end by outlining some algorithms of 1995 that solve this problem at a surprisingly low computational cost.

MSC:

65H05 Numerical computation of solutions to single equations
68W30 Symbolic computation and algebraic computation
65Y20 Complexity and performance of numerical algorithms
65-03 History of numerical analysis
12Y05 Computational aspects of field theory and polynomials (MSC2010)
30C15 Zeros of polynomials, rational functions, and other analytic functions of one complex variable (e.g., zeros of functions with bounded Dirichlet integral)
65E05 General theory of numerical methods in complex analysis (potential theory, etc.)
01-XX History and biography

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