Matlab数据插值与拟合

1、)()(1111iiiiiiiiixfxxxxxfxxxxFniiixlFxF1)()()(xli, 0)0(,)0(,)(1111111iiiiiiiiiiiiixxxixxxxxxxixxxxxxxxl略去略去1322211),(),(),()(nnnxxxxpxxxxpxxxxpxp)(xpi)()(1iiiixpxp)()(1iiiixpxp)()(1iiiixpxp 0)()(1 nxfxfniiixlyxL0)()()(xli)()()()()()()(110110niiiiiiniiixxxxxxxxxxxxxxxxxl function f = Language(x,y,x0)

2、%求已知数据点的拉格朗日多项式%已知数据点的x 坐标向量:x%已知数据点的y 坐标向量:y%为插值点的x坐标:x0%求得的拉格朗日多项式或x0处的插值:fsyms t;if(length(x) = length(y) n = length(x); else disp(x和y的维数不相等！); return;end %检错f = 0.0;for(i = 1:n) l = y(i); for(j = 1:i-1) l = l*(t-x(j)/(x(i)-x(j); end; for(j = i+1:n) l = l*(t-x(j)/(x(i)-x(j); %计算拉格朗日基函数 end; f = f

3、 + l; %计算拉格朗日插值函数 simplify(f); %化简 if(i=n) if(nargin = 3) f = subs(f,t,x0); %计算插值点的函数值 else f = collect(f); %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 endend1110210110,kmkmkmkxxxxxfxxxxfxxxxf)(00 xfxf000)()(,xxxfxfxxfmmm)()(,)(,)(,)()(11010102100100nnxxxxxxxxxfxxxxxxxfxxxxfxfxN)(0 xf)(1xf)(2xf)

4、(3xf)(nxf,10 xxf,20 xxf,30 xxf,0nxxf,210 xxxf,310 xxxf,10nxxxf,3210 xxxxf,210nxxxxf,10nxxxf)()()(111inininxfxfxf)()()(211211inininxfxfxf)()()(111inininxfxfxf)(0 xf)(1xf)(2xf)(3xf),(2110fff)()()()(000iiiixfxfxfxf)(iixff ),(222),(2321fff),(2532fff),(),(122202fff),(223212fff),(333),(2333303fff)()(2)(1)()()(002000 xfntxftxftxfthxNxNnh01xxhtnt 0)(1)(21)(1)()()(20nnnnnxfnntxftxftxfthxNxN h01xxht0tnniiiiiiiyyyaxxhxH1)2)()()(iixyy )(iixyy21nijjjijixxxxhnijjjiixxa11)()(10NmxaxaaxPmm20)(iNimjjijyxa mmmmmmmb