Nevilles Method for approximation

In summary, the conversation is about approximating a function f(x) using given values and building a table to do so. The speaker is unsure of how to find certain values and has a question about filling the table. They also mention using the function f(x) = 3^x to approximate the square root of 3 and have figured out how to build the table through interpolating tables.
  • #1
emptymaximum
110
0
basically, i don't get it at all.
i understand that

x0 P0
P01
x1 P1 P012
P12
x2 P2

let's approximate f(x) where x is some number.

i have some Pi given and a Pi(i+1) and Pi(i+1)(i+2)
i also have the xi
i don't know what f(x) is, some unknown function.
how do i find the Pi(i+1)(i+2)?

one question i have is to fill the table.
i have another question where I'm supposed to approximate
[itex] \sqrt{3} [/itex] by using [itex] f(x) = 3^x [/itex] and i have values for x0 through x4, so being able to build that table and i'll be able to do that no problem right?

what i have done so far:
nothing, i don't know how to build the table. alls i want help with is table building please.
 
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  • #2
UPDATE:

i figured out how to make the table by interpolating tables given.
thanks anyways.
 

FAQ: Nevilles Method for approximation

What is Neville's Method for approximation?

Neville's Method is a mathematical algorithm used to approximate a function or set of data points. It involves constructing a polynomial that passes through a given set of points, and then using that polynomial to estimate the value of the function at a specific point within the given range.

How does Neville's Method work?

Neville's Method works by constructing a polynomial using a set of data points (x,y). The polynomial is created by using a combination of Lagrange polynomials, which are used to interpolate a polynomial that passes through the given points. The final polynomial is then used to estimate the value of the function at a specific point within the given range.

When is Neville's Method used?

Neville's Method is commonly used in numerical analysis and scientific computing, particularly in situations where an exact value for a function is difficult to obtain or unnecessary. It is also useful for approximating values of functions that are expensive to compute.

What are the advantages of using Neville's Method?

One of the main advantages of Neville's Method is that it provides a more accurate approximation compared to other methods, such as linear or quadratic interpolation. It also allows for the estimation of values outside of the given range, as long as the function is well-behaved within that range. Additionally, it is a relatively simple and efficient method to use.

What are the limitations of Neville's Method?

One limitation of Neville's Method is that it can only be used to approximate continuous functions. It also requires a sufficient number of data points in order to produce an accurate result. Additionally, the accuracy of the method can be affected by the distribution of the data points, with clustered points resulting in less accurate approximations.

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