On the Complexity of Polynomial Zeros
Copyright policy )On the Complexity of Polynomial Zeros
An algorithm for simultaneous approximation of all zeros of a polynomial introduced by Householder is considered. A modification suitable for parallel computation is proposed. The root-finding problem for a polynomial of degree \(n\), having zeros \(z_ i\), \(i=1,\dots,n\) is \(NC\)- reduced to finding a polynomial \(\alpha(z)\) such that \(| \alpha(z_{i+1})/\alpha(z_ i)|\leq 1-1/n^ c\), where \(c\) is a constant.
- University of Pisa Italy
polynomial root- finding, Complexity and performance of numerical algorithms, Zeros of polynomials, rational functions, and other analytic functions of one complex variable (e.g., zeros of functions with bounded Dirichlet integral), Computational aspects of field theory and polynomials, parallel complexity, Numerical computation of solutions to single equations, Parallel numerical computation, polynomial zeros, Euclidean scheme
polynomial root- finding, Complexity and performance of numerical algorithms, Zeros of polynomials, rational functions, and other analytic functions of one complex variable (e.g., zeros of functions with bounded Dirichlet integral), Computational aspects of field theory and polynomials, parallel complexity, Numerical computation of solutions to single equations, Parallel numerical computation, polynomial zeros, Euclidean scheme
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