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 \(1+\sqrt 2\).
scientific article; zbMATH DE number 1356180