How can I optimize numerical approximation with fewer samples?

In summary, the speaker is seeking assistance with reducing the number of samples used in a linear approximation problem. They mention using either MATLAB or Excel and express a desire to find the best set of samples for the most accurate approximation. The potential methods for choosing the samples are mentioned, as well as a question about the reason for reducing the sample size.
  • #1
galc81
1
0
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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  • #2
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.
 

FAQ: How can I optimize numerical approximation with fewer samples?

What is numerical approximation?

Numerical approximation is a method of estimating a value or solution to a mathematical problem using a series of calculations and algorithms. It is often used when an exact solution is not feasible or when the problem is too complex to solve analytically.

How is numerical approximation different from analytical methods?

Numerical approximation relies on numerical calculations and algorithms, while analytical methods use mathematical equations to solve problems. Numerical approximation can provide an approximate solution to complex problems, whereas analytical methods provide exact solutions.

What are some common techniques used in numerical approximation?

Some common techniques used in numerical approximation include Newton's method, bisection method, and the secant method. Other techniques include interpolation, extrapolation, and integration methods such as Simpson's rule.

When is numerical approximation used?

Numerical approximation is used in various fields, including engineering, physics, economics, and computer science. It is often used when dealing with complex systems or when an exact solution is not possible.

What are the advantages and disadvantages of numerical approximation?

The main advantage of numerical approximation is that it allows for the solution of complex problems that cannot be solved analytically. It also provides a quick and efficient way to estimate solutions. However, numerical approximation can be prone to error and may not always provide an accurate solution. It also requires knowledge of numerical methods and may be computationally intensive.

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