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1、埃特金插值functionf=Atken(x,y,x0)symst;if(length(x)==length(y))n=length(x);elsedisp;return;endy1(1:n)=t;for(i=1:n-1)for(j=i+1:n)y1(j)=y(j)*(t-x(i))/(x(j)-x(i))+y(i)*(t-x(j))/(x(i)-x(j));endy=y1simplify(y1);endif(nargin==3)f=subs(y1(n),'t',x0);elsesimplify(y1(n
2、));f=collect(y1(n));f=vpa(f,6);end特征多项式法functionl=Chapoly(A)%特征多项式法求矩阵特征值%已知矩阵：A%求得的矩阵特征值：lsymst;N=size(A);n=N(1,1);y=det(A-t*eye(n,n));l=solve(y);l=vpa(1,5);%functionf=Chebyshev(y,k,x0)symst;T(1:k+1)=t;T(1)=1;T(2)=t;c(1:k+1)=0.0;c(1)=int(subs(y,findsym(s
3、ym(y)),sym('t'))*T(1)/sqrt(1-t^2),t,-1,1)/pi;c(2)=2*int(subs(y,findsym(sym(y)),sym('t'))*T(2)/sqrt(1-t^2),t,-1,1)/pi;f=c(1)+c(2)*t;fori=3:k+1T(i)=2*t*T(i-1)-T(i-2);c(i)=2*int(subs(y,findsym(sym(y)),sym('t'))*T(i)/sqrt(1-t^2),t,-1,1)/2;f=f+c(i)*T(i);f=vpa(
4、f,6);if(i==k+1)if(nargin==3)f=subs(f,'t',x0);elsef=vpa(f,6);endendend弦割法求解非线性方程function[xkt]=ChordsecantToEquation(f,x0,x1,eps)%弦割法求解非线性方程%[xkt]=ChordsecantToEquation(f,x0,x1,eps)%x:近似解%k:迭代次数%t:运算时间%f:原函数，定义为内联函数%x0,x1:初始值%eps:误差限%%应用举例：%f=inline('x^3+4*
5、x^2-10');%x=ChordsecantToEquation(f,1,2,0.5e-6)%[xk]=ChordsecantToEquation(f,1,2,0.5e-6)%[xkt]=ChordsecantToEquation(f,1,2,0.5e-6)%函数的最后一个参数也可以不写，默认情况下，eps=0.5e-6%[xkt]=ChordsecantToEquation(f,1,2)ifnargin==3eps=0.5e-6;endtic;k=0;while1x=x1-f(x1)*(x1-x0).
6、/(f(x1)-f(x0));k=k+1;ifabs(x-x1)7、
8、k>30break;endx0=x1;x1=x;endt=toc;ifk>=30disp('迭代次数太多。');x=0;t=0;end复合求积公式function[I,step]=CombineTraprl(f,a,b,eps)%f被积函数%a,b积分上下限%eps精度%I积分结果%step积分的子区间数if(nargin==3)eps=1.0e-4;endn=1;h=(b-a)/2;I1=0;I2=(subs(sym(f),fi
9、ndsym(sym(f)),a)+subs(sym(f),findsym(sym(f)),b))/h;whileabs(I2-I1)>epsn=n+1;h=(b-a)/n;I1=I2;I2=0;fori=0:n-1x=a+h*i;x1=x+h;I2=I2+(h/2)*(subs(sym(f),findsym(sym(f)),x)+subs(sym(f),findsym(sym(f)),x1));endendI=I2;step=n;functionf=DCS(x,y,x0)symst;if(length(x
10、)==length(y))n=length(x);c(1:n)=0.0;elsedisp('x和y的维数不相等！');return;endc(1)=y(1);for(i=1:n-1)for(j=i+1:n)y1(j)=(x(j)-x(i))/(y(j)-y(i));endc(i+1)=y1(i+1);y=y1;endf=c(n);for(i=1:n-1)f=c(n-i)+(t-x(n-i))/f;f=vpa(f,6);if(i
