拉格朗日差值、牛顿插值以及三次样条插值的matlab实现.pdfVIP

拉格朗日差值、牛顿插值以及三次样条插值的matlab实现

%Lagrange插值

clear

clc

%

n=10;%结点个数

lb=-1;%下界

ub=1;%上界

step=0.01;%作图点步长

%

%原始函数图形

x0=lb:step:ub;

y0=1./(1+25*x0.^2);

plot(x0,y0,r-);

holdon

%

%插值函数

fori=1:n+1

xi(i)=lb+(ub-lb)*(i-1)/n;

yi(i)=1/(1+25*xi(i)^2);

end

%

count=1;

forx=lb:step:ub

fl=0;

%

%求出pn(xk)

fork=1:n+1

up=1;

dn=1;

%

%求出f(xk)

fori=1:n+1

ifk~=i

up=up*(x-xi(i));

dn=dn*(xi(k)-xi(i));

end

end

%

fl=fl+yi(k)*up/dn;

end

pn(count)=fl;

%

fi(count)=1/(1+25*x^2);%求原函数的值

count=count+1;

end

%

%L插值函数图

x=lb:step:ub;

plot(x,pn,g--)

%

num=(ub-lb)/step+1;

fori=1:num

p_f(i)=pn(i)-fi(i);

end

center=fix(num/2);

scale=fix(num/10);

a=center-scale;

b=center+scale;

disppn(i)-fi(i)的值为：

p_f(a:b)%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%%

clearall

clc

%Newton迭代法求解极小值点

%=====================================

disp几点说明：

disp1.程序中的函数采用课本P102例3.3.2。

disp2.只需改变所需要求的函数和初始点的值。

disp

=========================================

==========

%=====================================

%定义函数

disp函数f(x)为:

symsx1x2

f=(x1-2)^4+(x1-2)^2*x2^2+(x2+1)^2

disp初始点的值：

x0=[1;1]

%=====================================

%求函数的梯度和海色阵

disp函数f的梯度：

g=jacobian(f,[x1;x2])

disp函数f的Hesse矩阵：

G=jacobian([g(1);g(2)],[x1,x2])

%=====================================

%定义迭代的最大次数

n=10;

%=====================================

%一些初始值的计算

g0=subs(g,{x1,x2},{x0(1),x0(2)});

G0=subs(G,{x1,x2},{x0(1),x0(2)});

f0=subs(f,{x1,x2},{x0(1),x0(2)});

%=====================================

%