从图形（不是Hermite）中识别Mathematica插值函数
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我正在反向工程Mathematica如何进行列表插值：
(* Fortunately, Mathematica WILL interpolate an arbitrary list *)
tab = Table[a[i], {i,1,100}]
f = Interpolation[tab]
(* get the coefficient of each term by setting others to zero *)
Plot[{f[42+x] /. {a[42] -> 0, a[43] ->0, a[44] -> 0, a[41] -> 1}},
{x,0,1}]
Plot[{f[42+x] /. {a[41] -> 0, a[43] ->0, a[44] -> 0, a[42] -> 1}},
{x,0,1}]
Plot[{f[42+x] /. {a[42] -> 0, a[41] ->0, a[44] -> 0, a[43] -> 1}},
{x,0,1}]
Plot[{f[42+x] /. {a[42] -> 0, a[43] ->0, a[41] -> 0, a[44] -> 1}},
{x,0,1}]
(* above is neither Hermite, nor linear, though some look close *)
(* these are available at oneoff.barrycarter.info/STACK/ *)
Table[f[42+x] /. {a[42] -> 0, a[43] ->0, a[44] -> 0, a[41] -> 1},
{x,0,1, 1/100}] >> /home/barrycarter/BCINFO/ONEOFF/STACK/coeff41.txt
Table[f[42+x] /. {a[41] -> 0, a[43] ->0, a[44] -> 0, a[42] -> 1},
{x,0,1, 1/100}] >> /home/barrycarter/BCINFO/ONEOFF/STACK/coeff42.txt
Table[f[42+x] /. {a[41] -> 0, a[42] ->0, a[44] -> 0, a[43] -> 1},
{x,0,1, 1/100}] >> /home/barrycarter/BCINFO/ONEOFF/STACK/coeff43.txt
Table[f[42+x] /. {a[41] -> 0, a[42] ->0, a[43] -> 0, a[44] -> 1},
{x,0,1, 1/100}] >> /home/barrycarter/BCINFO/ONEOFF/STACK/coeff44.txt
(x-2)*(x-1)*x/-6
(x-2)*(x-1)*(x+1)/2
x*(x+1)*(x-2)/-2
(x-1)*x*(x+1)/6
没有找到相关结果
已邀请:
1 个回复
喷乡顾沥沪
test[n_, i_] := Module[{x = ConstantArray[0,n]},x[[i]] = 1; x]With[{a=1, b=2.5, n=5, i=2, j=3}, Plot[{Interpolation[a test[n,i] + b test[n,j]][x], a Interpolation[test[n,i]][x] + b Interpolation[test[n,j]][x]}, {x, 1, n}] ]With[{n=7, ioMax = 5}, Table[ Module[{fns}, fns = Table[Interpolation[test[n,i], InterpolationOrder->io], {i,1,n}]; Table[Plot[Evaluate@D[f[#], {#,io}]&[x], {x,1,n}, PlotRange->Full, PlotStyle->Thick, ImageSize->150], {f, fns}] ], {io, 1, ioMax} ] ] // TableForm