matlab函数求极值.ppt

单击此处编辑母版标题样式,单击此处编辑母版文本样式,第二级,第三级,第四级,第五级,*,*,*,函数的极值,1,、一元函数的极值,函数命令：,fminbnd,调用格式：,x,feval,exitflag,output=fminbnd(fun,x1,x2,options),%,求,fun,在区间,(x1,x2),上的极值,.,返回值：,x:,函数,fun,在,(x1,x2),内的极值点,feval:,求得函数的极值,exitflag:,exitflag0,函数收敛于解,x,处,exitflag=0,已达最大迭代次数,exiflag,A=fsolve(myfsolve2,ones(3)%,ones,（,3,）初始矩阵，直全为,1,myfsolve2(A),4,、数值积分,函数命令：,quad,quadl,odbquad,调用格式,:,q1=,quad(fun,a,b,tol,),%,采用自适应,Simpson,算法计算积分,q1=,quadl(fun,a,b,tol,),%,采用自适应,Lobatto,算法计算积分,q2=,dblquad(fun,xmin,xmax,ymin,ymax,tol,),%,二重积分,q3=,triplequad(fun,xmin,xmax,ymin,ymax,zmin,zmax,tol,),%,三重积分,例,1,：求,I,=,.,(1),利用,quad,quadl,计算,format long,I=quad(exp(-x.2),0,1,1e-8),Il=quadl(exp(-x.2),0,1,1e-8),I=,0.74682413285445,Il=,0.74682413398845,(2),采用编程计算,:,function I=myquad1(a,b,n),x=,linspace(a,b,n,);%,把,ab,区间平均分成,n,等份,y=exp(-x.2)*(,b-a)/n,;,%,高,底,=,每个取边梯形的面积,I=sum(y);,I1=myquad1(0,1,10000),I2=myquad1(0,1,100000),I1=,0.74681784375801,I2=,0.74682350396218,例,2,：计算,利用,dblquad,s1=dblquad(x.y,0,1,1,2),%,被积函数写成数组的形式,db_(double),二重积分，即两次积分,s1=,0.40546626724351,s2=dblquad(x,y)x.y,0,1,1,2),%,采用匿名函数表示被积函数,x y,的区间,s2=,0.40546626724351,s3=dblquad(inline(x.y),0,1,1,2),s3=,0.40546626724351,求,s1=,s2=,s3=,例,3,：,syms x,x,符号变量,f1=1/(1+x2);,f2=1/(x2+2*x+3);,f3=1/(x2+2*x-3);,s1=int(f1,1,inf),1,到正无穷,s2=int(f2,-inf,inf),int,符号积分,s3=int(f3,-inf,inf),s1=,1/4*pi,s2=,1/2*pi*2(1/2),s3=,NaN,不确定的结果,s4=quad(1./(1+x.2),1,inf),%quad,只能计算闭型积分,Warning:Infinite or Not-a-Number function value encountered.,In quad at 95,s4=,NaN,s5=quad(1./(1+x.2),1,10),s5=,0.6857,s6=int(f1,1,10),s6=,atan(10)-1/4*pi,vpa(s6,10),ans=,.6857295105,