matlab代碼--插值.docVIP

插值 1.Atken求已知数据点的艾特肯插值多项式 function f = Atken(x,y,x0) syms t; if(length(x) == length(y)) n = length(x); else disp(x和y的维数不相等！); return; end %检错 y1(1:n) = t; %符号函数数组要赋初值 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)); end y = y1; simplify(y1); end if(nargin == 3) f = subs(y1(n),t,x0); %计算插值点的函数值 else simplify(y1(n)); %化简 f = collect(y1(n)); %将插值多项式展开 f = vpa(f,6); %将插值多项式的系数化成6位精度的小数 end BSample求已知数据点的第一类B样条的插值 function f0 = BSample(a,b,n,y,y_1,y_N,x0) f0 = 0.0; h = (b-a)/n; c = zeros(n+3,1); b = zeros(n+1,1); for i=0:n-1 if(a+i*h=x0) (a+i*h+h=x0) index = i; break; end end %找到x0所在区间 A = diag(4*ones(n+1,1)); I = eye(n+1,n+1); AL = [I(2:n+1,:);zeros(1,n+1)]; AU = [zeros(1,n+1);I(1:n,:)]; A = A+AL+AU; %形成系数矩阵 for i=2:n b(i,1) = 6*y(i); end b(1) = 6*y(1)+2*h*y_1; b(n+1) = 6*y(n+1)-2*h*y_N; d = followup(A,b); %用追赶法求出系数 c(2:n+2) = d; c(1) = c(2) - 2*h*y_1; %c(-1) c(n+3) = c(3)+2*h*y_N; %c(n+1) x1 = (a+index*h-h-x0)/h; m1 = c(index+1)*(-((abs(x1))^3)/6+(x1)^2-2*abs(x1)+4/3); x2 = (a+index*h-x0)/h; m2 = c(index+2)*((abs(x2))^3/2-(x2)^2+2/3); x3 = (a+index*h+h-x0)/h; m3 = c(index+3)*((abs(x3))^3/2-(x3)^2+2/3); x4 = (a+index*h+2*h-x0)/h; m4 = c(index+4)*(-((abs(x4))^3)/6+(x4)^2-2*abs(x4)+4/3); f0 = m1+m2+m3+m4; %求出插值 DCS用倒差商算法求已知数据点的有理分式形式的插值分式 function f = DCS(x,y,x0) syms t; if(length(x) == length(y)) n = length(x); c(1:n) = 0.0; else disp(x和y的维数不相等！); return; end c(1) = y(1); for(i=1:n-1) for(j=i+1:n) y1(j) = (x(j)-x(i))/(y(j)-y(i)); end c(i+1) = y1(i+1); y = y1; end f = c(n); for(i=1:n-1) f = c(n-i) + (t-x(n-i))/f; f = vpa(f,6); if(i==n-1) if(nargin == 3) f =