Solution of Algebraic Equations

Algebraic equations are routinely encountered while modeling problems in various areas of engineering. Finding the solution of such equations is also referred to as “root” finding or finding the “zeroes” of the equation. Sometimes equations occur as simultaneous equations and the solution of such equations is extremely important in engineering applications. Such solutions represent operating point(s) of an engineering system, as will be made clear later on. Several methods of root finding listed below will be considered here. • Bisection method • Fixed point iteration method • Gauss Seidel iteration method for a set of nonlinear equations • Newton Raphson amethod • Secant method • Regula falsi method We also consider optimization problems since they are essentially root finding problems