Re: Points to Funciton

• To: mathgroup at smc.vnet.net
• Subject: [mg8663] Re: Points to Funciton
• From: Daniel Lichtblau <danl>
• Date: Mon, 15 Sep 1997 02:48:51 -0400
• Organization: Wolfram Research, Inc.
• Sender: owner-wri-mathgroup at wolfram.com

```MJ.Stone at solaris.cc.vt.edu wrote:
>
> If I have a series of coordinates, is it possible to use mathematica
> to find a function that will satisfy these coordinates?  If so, how?

In Mathematica one can use InterpolatingPolynomial.

In[4]:= ??InterpolatingPolynomial
InterpolatingPolynomial[data, var] gives a polynomial in the variable
var
which provides an exact fit to a list of data. The data can have the
forms
{{x1, f1}, {x2, f2}, ... } or {f1, f2, ... }, where in the second
case, the
xi are taken to have values 1, 2, ... . The fi can be replaced by
{fi, dfi,
ddfi, ... }, specifying derivatives at the points xi.
Attributes[InterpolatingPolynomial] = {Protected}

For example,

In[5]:= InterpolatingPolynomial[{{-2,5}, {1,4}, {6,2}, {8,-7}, {9,1}},
x]
1        1         97     73 (-8 + x)
Out[5]= 5 + (-(-) + (-(---) + (-(----) + -----------) (-6 + x)) (-1 +
x))
3       120       1680       1232
>     (2 + x)

In[6]:= Expand[%]

2         3       4
782    6103 x   13407 x    1093 x    73 x
Out[6]= -(---) + ------ + -------- - ------- + -----
385     1320      6160      1320     1232

Daniel Lichtblau
Wolfram Research
danl at wolfram.com

```

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