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MathGroup Archive 2003

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Re: Interpolation with random nodes

  • To: mathgroup at smc.vnet.net
  • Subject: [mg44788] Re: Interpolation with random nodes
  • From: Bill Rowe <browe51 at earthlink.net>
  • Date: Thu, 27 Nov 2003 11:38:12 -0500 (EST)
  • Sender: owner-wri-mathgroup at wolfram.com

On 11/25/03 at 12:45 AM, a_d_u_n at o2.pl (Wojtek) wrote:

> I want to interpolate function with a few different sets of nodes.
> One of them are random ones. I have made the list of nodes and my function's
> values:

> (n is given)

> data1=Table[{e=Random[]*2-1,ArcTan(x,0.,n}]

I assume what you mean is something like:

data1 = Table[{x = Random[]*2-1, ArcTan@x, {n}]
 
> and I have a list: {{x_0,f(x_0)},{x_1,f(x_1)}...}

> I use the following formula to calculate my function

> L(x) = SUM(j=0..n) f(x_j) * Lambda(j,x)

> And I need to extract these values from my list.
 
> and I want to define two functions
 
> y[n] - this returns the f(x_n) from my list
> x[n] - this returns the x_n from my list
 
> how can I do it in mathematica?

Given the structure of your list there are a number of ways to extract x and y as you've defined them above. Any of the following will work

x = First/@data1;
y = Last/@data1;


x = data1[[All,{1}]];
y = data1[[All,{2}]];

{x,y} = Transpose@data1;


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