Introduction to Numerical Analysis (original) (raw)

Methods for approximating solutions of nonlinear algebraic equations are outlined, focusing on the case of finding roots for a single variable equation. The discussion emphasizes iterative methods and the importance of identifying intervals in which roots may exist, leveraging continuity and the Intermediate Value Theorem. The text also mentions the limitations of exact analytical solutions for polynomials of higher degrees and the necessity of approximation methods when dealing with arbitrary functions.