Analysis of the quasi-Laguerre method
Copyright policy )Analysis of the quasi-Laguerre method
The quasi-Laguerre method is an iterative process for finding real or complex roots of a polynomial \(p\). It is based on the logarithmic derivative \(q={p'\over p}\) and starts with two values \(x_0\), \(x_1\) and the logarithmic derivatives \(q_0\), \(q_1\) at \(x_0\) and \(x_1\), respectively. The author presents three derivations of his method and proves theoretical results concerning global and local convergence and monotonicity of the sequence of iterates. In addition, he shows that under suitable conditions the convergence order of the method is \(1+\sqrt 2\).
- University of Rochester United States
- Oakland University United States
quasi-Laguerre method, convergence, iterative method, Zeros of polynomials, rational functions, and other analytic functions of one complex variable (e.g., zeros of functions with bounded Dirichlet integral), roots of polynomials, Computational aspects of field theory and polynomials, Numerical computation of solutions to single equations, monotonicity, Real polynomials: location of zeros
quasi-Laguerre method, convergence, iterative method, Zeros of polynomials, rational functions, and other analytic functions of one complex variable (e.g., zeros of functions with bounded Dirichlet integral), roots of polynomials, Computational aspects of field theory and polynomials, Numerical computation of solutions to single equations, monotonicity, Real polynomials: location of zeros
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