ABSTRACT
The solutions to linear algebraic equations have been discussed extensively in Chapter 4. However, most frequently encountered are nonlinear equations in sciences and engineering problems. Solving nonlinear equations could be computationally expensive; therefore, the solving of approximate linear equations was indispensable especially in the early times when the computers were not powerful enough. Today, with the rapid development of computing technology, solving directly nonlinear equations is becoming increasingly important. In this chapter, we will focus on MATLAB solutions to nonlinear equations and optimization problems. In Section 6.1, solutions to nonlinear algebraic equations will be presented. The graphical method for nonlinear equations with one and two unknown variables will be given first, and quasi-analytical solutions will be studied for polynomial equations and equations convertible to polynomial equations. Numerical solutions to nonlinear equations and nonlinear matrix equations will also be discussed in this section.
