Estimating roots of polynomials using perturbation theory

摘要

Perturbation theory and the order of magnitude of terms are employed to develop two theorems. The theorems may be useful to estimate the order of magnitude of the roots of a polynomial a priori before solving the equation. The theorems are developed for two special types of polynomials of arbitrary order with their coefficients satisfying certain conditions. Numerical applications of the theorems are presented as examples.