Approximate Zeros of Quadratically Convergent Algorithms
Copyright policy )Approximate Zeros of Quadratically Convergent Algorithms
Smale’s condition for a point to be an approximate zero of a function for Newton’s method is extended to the general quadratically convergent iterative algorithm. It is shown in which way the bound in the condition is affected by the characteristics of the algorithm. This puts the original condition of Smale for Newton’s method in a more general perspective. The results are also discussed in the light of numerical evidence.
General theory of numerical methods in complex analysis (potential theory, etc.), Complexity and performance of numerical algorithms, Newton's method, iterative algorithm, efficiency, Zeros of polynomials, rational functions, and other analytic functions of one complex variable (e.g., zeros of functions with bounded Dirichlet integral), Numerical computation of solutions to single equations, complexity, zeros of holomorphic functions, quadratic convergence
General theory of numerical methods in complex analysis (potential theory, etc.), Complexity and performance of numerical algorithms, Newton's method, iterative algorithm, efficiency, Zeros of polynomials, rational functions, and other analytic functions of one complex variable (e.g., zeros of functions with bounded Dirichlet integral), Numerical computation of solutions to single equations, complexity, zeros of holomorphic functions, quadratic convergence
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