多项式求值的MATLAB实现

Posted 2020-10-12 温酒待君归

公茂果老师的课件中，给出了四种多项式求值的算法，下面给出代码示例：

课件地址：http://see.xidian.edu.cn/faculty/mggong/chn.htm

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%E-mail: [e-mail]
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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;
    

 

 下面是结果的显示：

参考链接   https://wenku.baidu.com/view/c3f6f2b8c5da50e2534d7f42.html

             https://wenku.baidu.com/view/be4e3335b0717fd5370cdc40.html