多项式求值的MATLAB实现

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%E-mail: jtailong@163.com
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num=[10 50 100 150 200 300 400 500 10000 20000 50000 100000]; 

x=input(‘please enter x:‘) %求解相应x的多项式的值

for m=1:1:12 %从1至12，步长为1 

    a=rand(1,num(m)+1); %生成相应的序列a
   %方法一：直接代入法
    tic; %开始计时
    p1(m)=polyval(a,x); 
    t1(m)=toc;  
    
    %方法二:递归法一
    tic;
    p2(m)=0;
    for j=1:1:(num(m)+1)
    p2(m)=p2(m)+a(j)*x^(j-1);
    end
    t2(m)=toc;
    
    %方法三：递归法二
    tic;
    p3(m)=0;
    q=1;
    for j=1:1:(num(m)+1)
        q=q*x;
        p3(m)=p3(m)+a(j)*q;
    end
    t3(m)=toc;
    
    %方法四：递归法四
    
    tic;
    p4(m)=0;
    for j=1:num(m)
        p4(m)=x*p4(m)+a(num(m)+2-j); %百度文库中出现的算法，会漏掉一个点值
    end
    t4(m)=toc;
end
%画图
g=semilogx(num,t1,‘r+‘,num,t2,‘b*‘,num,t3,‘g:‘,num,t4,‘k-.‘);
legend(‘一‘,‘二‘,‘三‘,‘四‘);
set(g,‘linestyle‘,‘:‘,‘linewidth‘,2.0,‘markersize‘,8);
xlabel(‘num=10 ,50 ,100 ,150 ,200, 300 ,400, 500 ,10000, 20000, 50000 ,100000‘);
ylabel(‘time‘);
title(‘温酒待君归四线比较图‘)
grid on;