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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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