A Generalization of Obreshkoff-Ehrlich Method for Multiple Roots of Algebraic, Trigonometric and Exponential Equations

TL;DR

This paper introduces a generalized iterative method with cubic convergence for simultaneously finding all roots, including multiple roots, of algebraic, trigonometric, and exponential equations, improving efficiency over existing methods.

Contribution

It extends the Obreshkoff-Ehrlich method to handle multiple roots in various types of equations with cubic convergence and similar computational effort as methods for simple roots.

Findings

Achieves cubic convergence for multiple roots

Applicable to algebraic, trigonometric, and exponential equations

Comparable computational complexity to methods for simple roots

Abstract

In this paper methods for simultaneous finding all roots of generalized polynomials are developed. These methods are related to the case when the roots are multiple. They possess cubic rate of convergence and they are as labour-consuming as the known methods related to the case of polynomials with simple roots only.