插值法 2010年10月24日 11:16 牛顿插值与拉格朗日插值ployfit实现多项式回归matlab的m文件： Function yint=newtint(x,y,xx) %newtint:newton interpolating polynomial %yint=newtint(x,y,xx):uses an (n-1)-order newton %to determine a value of the dependent variable (yint) %at a given value of the independent variable,xx. %input: %x=independent variable %y=dependent variable %xx=value of independent variable at which Interpolation is calculated % output: % yint=interpolated value of dependent variable %compute the finite divided differences in the form of a %difference table n=length(x); If length(y)~=n,error('x and y must be same length'); End b=zeros(n,n); %assign dependent variables to the first column of b. b(:,1)=y(:);%the(:)ensures that y is a column vector. For j=2:n For i=1:n-j+1 b(I,j)=(b(i+1,j-1)-b(I,j-1))/(x(i+j-1)-x(i)); End End % use the finite divided differences to interpolate Xt=1; Yint=b(1,1); For j=1:n-1 xt=xt*(xx-x(j)); Yint=yint+b(1,j+1)*xt; End ------------------------------------------------------------------------------------------------------------- 拉格朗日插值方法m文件的编写 Function yint =lagrange(x,y,xx) %lagrange:lagrange interpolating polynomial %yint=lagrange(x,y,xx):uses an (n-1)-order % to determine a value of the dependent variable (yint) at % a given value of the independent variable ,xx. %input: % x=independent variable %y=dependent variable %xx=value of independent variable at which the interpolation is calculated %output: % yint=interpolated value of dependent variable n=length(x); If length(y)~=n,error('x and y must be same length'); End s=0; For i=1:n Product=y(i); For j=1:n If i~=j Product =product*(xx-x(j))/(x(i)-x(j)); End 分区 新分区 1 的第 1 页 

End End s=s+product; End Yint=s; 分区 新分区 1 的第 2 页