Equations

Abstract

Solving an equation is one of the prime topics of elementary algebra, where it is a powerful tool for problem solving, whenever algebraic formulation is possible. Equations appear in advanced sciences as well in a variety of ways, mostly in complicated forms. Developing efficient computational schemes for solution in a general manner is therefore of paramount importance. It is emphasised that through these schemes only approximate numerical solutions are sought, that may never be exact. In a sense it is useless to think of exact solutions because equations arising in practice always contain experimentally determined parameters that are always contaminated by errors of measurement. Even if it is assumed that an equation is exactly given, machine computation of the solution following any method, invites roundoff errors.