Divided Difference Table - Guidance

[Seeker555]

Given points

x_j

and associated function values

f(x_j)

define the first order divided difference and then the higher order divided differences.

I get it's asking for general definitions not a specific answer obviously. If it were a specific divided difference question I'd draw a table based off the xj and f(xj) values and i guess each point in the triangle on it's side ie the table would be the each divided difference order the first calculation column being order 1 and then the next order 2. I guess i'm just not sure about how I answer the question because it doesn't seem like the explanation I just gave then would be what they want considering it's a preparation exam question worth 4 marks. Thanks.

 

[mmm4444bot]

Let the subscript j take on some specific values.

Are you able to work with these symbolic numbers?

x0	f(x0)
x1	f(x1)
x2	f(x2)
x3	f(x3)

i guess each point in the triangle on it's side ie the table would be the each divided difference order the first calculation column being order 1 and then the next order 2

I'm not sure what the triangle is about, and I find the English statement above difficult to resolve.

 

[Seeker555]

I was writing in French but that aside, by triangle I mean the divided difference table. Whereby each column is the order of the divided difference, with the left most column being order 1 and then the column to it's right being order 2 and so forth. But do you think that is what they're accepting as an answer for a definition, or what do you think is the best definition?

 

[mmm4444bot]

Well, if you're planning on writing out a table, you need to use something to the represent the entries.

No, I'm not sure what they want. As they asked you to use x_j and f(x_j), my guess is for the standard definition. I'm think that you can find it on Wikipedia or university web pages;
try googling keywords: definition divided differences .

This type of definition does not require a table.

Look for symbolism that matches the function notation that you've been asked to use.