Matlab數(shù)據(jù)插值與擬合

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、%求已知數(shù)據(jù)點(diǎn)的拉格朗日多項(xiàng)式%已知數(shù)據(jù)點(diǎn)的x 坐標(biāo)向量:x%已知數(shù)據(jù)點(diǎn)的y 坐標(biāo)向量:y%為插值點(diǎn)的x坐標(biāo):x0%求得的拉格朗日多項(xiàng)式或x0處的插值:fsyms t;if(length(x) = length(y) n = length(x); else disp(x和y的維數(shù)不相等！); return;end %檢錯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); %計算拉格朗日基函數(shù) end; f = f

3、 + l; %計算拉格朗日插值函數(shù) simplify(f); %化簡 if(i=n) if(nargin = 3) f = subs(f,t,x0); %計算插值點(diǎn)的函數(shù)值 else f = collect(f); %將插值多項(xiàng)式展開 f = vpa(f,6); %將插值多項(xiàng)式的系數(shù)化成6位精度的小數(shù) 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