MHB How can I optimize numerical approximation with fewer samples?

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To optimize numerical approximation with fewer samples, one approach is to divide the independent variable domain into equal-width segments and select endpoints as samples. However, the challenge lies in ensuring that these selected points are representative of the data available. Reducing sample size may compromise the accuracy of predictions, as larger sample sizes typically enhance statistical power. The discussion raises a critical question about the necessity of reducing samples when tools like Excel can handle larger datasets effectively. Ultimately, careful consideration is needed to balance sample size and approximation accuracy.
galc81
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Hi all,
i have a problem to solve that i want maybe to solve with MATLAB o excel.
I have a numerical samples and with linear approsimation i have a function, but now i want to use less samples for example only 20 and i want to find the best set of samples to approsimate in the best way the function.
thanks a lot
 
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galc81 said:
Hi all,
i have a problem to solve that i want maybe to solve with MATLAB o excel.
I have a numerical samples and with linear approsimation i have a function, but now i want to use less samples for example only 20 and i want to find the best set of samples to approsimate in the best way the function.
thanks a lot

Well, I suppose there are a number of ways you could choose your samples: break up the independent variable domain into 19 equal-width chunks, and use the endpoints (20 of them) as your samples. You might or might not have data for those points, naturally, so you could choose the ones closest to those that you do have.

The big question in my mind is this: from a statistics perspective, you usually want the largest sample size you can get, because your predictions and descriptive power are always greater when you have a larger sample size. So why do you want to reduce the size of your sample? Excel, for example, can crunch through quite a large sample size.
 

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