高等应用数学问题的MATLAB求解06.ppt

Chapter6

NonlinearEquationsandOptimizationProblemsSolvingAppliedMathematicalProblemswithMATLABCRC/TaylorFrancisPressChineseversionbyTsinghuaUniversityPressPPTbyWenbinDongandJunPeng,NortheasternUniversity,PRCProofreadbyDingyuXueYangQuanChen星期四,2008-4-24,22:08:13

Chapter6

NonlinearEquationsandOptimizationProblemsSolutionstoNonlinearAlgebraicEquationsSolvingUnconstrainedOptimizationProblemsSolvingConstrainedOptimizationProblemsSolvingMixedIntegerProgrammingProblemsLinearMatrixInequalities5/26/2025

6.1SolutionstoNonlinearAlgebraicEquationsGraphicalmethodforsolvingnonlinearequationsQuasi-analyticalsolutionstopolynomial-typeequationsNumericalsolutionstoordinarynonlinearequationsSolutionstononlinearmatrixequations5/26/2025

6.1.1GraphicalmethodforsolvingnonlinearequationsGraphicallysolvingnonlinearequationsofasinglevariableGraphicallysolvingnonlinearequationsoftwovariablesNotsuitablemoreequationswithmorevariables5/26/2025

GraphicallysolvingnonlinearequationsofasinglevariableThefunctionezplot()canbeusedtodrawthecurvesfromtheimplicitfunction.Therealsolutionstotheequationscanberetrievedfromtheintersectionsofthecurveswith5/26/2025

Example6.1Graphicallysolve:MATLABcommands:Verification:5/26/2025

GraphicallysolvingnonlinearequationsoftwovariablesUseezplot()functiontodrawthealltheequations.Theintersectionsofthecurvesarethenthesolutionstotheoriginalsimultaneousequations5/26/2025

Example6.2Graphicallysolvethefollowing:Plotofthefirstfunction:Plotofthesecondfunction:5/26/2025

Therectangularregioncanbeselected5/26/2025

6.1.2Quasi-analyticalsolutionstopolynomial-typeequationsSpecialequationssuchaspolynomialequations,maybeofhighorderAbel-RuffiniTheoremclaimthatnoanalyticalsolutionmethodfor5+thorderequationNumerical