高等应用数学问题的MATLAB求解06.ppt

Slide 1 (of 11) Chapter 6Nonlinear Equations and Optimization Problems Chapter 6 Nonlinear Equations and Optimization Problems Solutions to Nonlinear Algebraic Equations Solving Unconstrained Optimization Problems Solving Constrained Optimization Problems Solving Mixed Integer Programming Problems Linear Matrix Inequalities 6.1 Solutions to Nonlinear Algebraic Equations Graphical method for solving nonlinear equations Quasi-analytical solutions to polynomial-type equations Numerical solutions to ordinary nonlinear equations Solutions to nonlinear matrix equations 6.1.1 Graphical method for solving nonlinear equations Graphically solving nonlinear equations of a single variable Graphically solving nonlinear equations of two variables Not suitable more equations with more variables Graphically solving nonlinear equations of a single variable The function ezplot() can be used to draw the curves from the implicit function . The real solutions to the equations can be retrieved from the intersections of the curves with Example 6.1 Graphically solve : MATLAB commands: Verification: Graphically solving nonlinear equations of two variables Use ezplot() function to draw the all the equations. The intersections of the curves are then the solutions to the original simultaneous equations Example 6.2 Graphically solve the following: Plot of the first function: Plot of the second function: The rectangular region can be selected 6.1.2 Quasi-analytical solutions to polynomial-type equations Special equations such as polynomial equations, may be of high order Abel-Ruffini Theorem claim that no analytical solution method for 5+th order equation Numerical solution not accurate High precision methods exist Many equations can be converted into polynomial equations Example 6.3 Graphically solve MATLAB command solutions: The syntax to solve polynomial-type equations the simplest direct solutions variables specifi