       Re: Approximation of a Function

• To: mathgroup at smc.vnet.net
• Subject: [mg33474] Re: Approximation of a Function
• From: Thomas Burton <tburton at brahea.com>
• Date: Fri, 22 Mar 2002 04:07:09 -0500 (EST)
• Sender: owner-wri-mathgroup at wolfram.com

```Hi,

You can choose the interval, model, and fitting criterion, but you will be
stuck the goodness of fit determined by these choices. Here I choose your
suggested model, the interval [0.1, 1], and default measure of fit,
unweighted sum of squares of deviations, over equally spaced points on the
interval.

In:= <<Statistics`NonlinearFit`

In:= Clear[a,b,c,f,g,c1,c2,x]

In:= f[x_]:=a*x+b*x^2+c*x^3

In:= g[x_]:=c1 x^c2

In:= Block[{a=1,b=2,c=3},
NonlinearFit[Table[{x,f[x]},{x,0.1,1,.1}],g[x],{x},{c1,c2}]
]
Out= 5.92041141648034*x^2.124715956132496

Tom Burton

On 3/21/02 6:36 AM, in article a7cr53\$hsn\$1 at smc.vnet.net, "Zsolt Regaly"
<rezso at Amalthea.elte.hu> wrote:

> Hi MathGroup!
>
> Can somebody to help me to find a solution of approximation of a function?
> I have a function f[x_]:=a*x+b*x^2+c*x^3, where a,b,c are known numbers. I
> would like to find a simplier function for f, for example g[x]=c1 x^c2 at an
> given interval with specified precision. How can I find the numbers c1 and c2?
>
> Thanks for Help, Zsolt Regaly.
>

```

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