Can the method of Finite Differences be used with non-sequential x-values?
| 1 | 3 | 6 | 10 | 15 | 21 | 28 | 36 | 45 |
| 24 | 49 | 74 | 99 | 124 | 149 | 174 | 199 | 224 |
Above is a table representing a polynomial function
+33654 Is the first line meant to be the x-values and the second line the y-values? (Actually, the values in each line are sequential, though not with a constant interval in the case of the first line.)
If so, I suggest you first use your method of differences on each line separately to find x in terms of n (the position number of the items : for n = 1, 2, 3, 4 etc x = 1, 3, 6, 10, etc.
Then eliminate n from the two equations to get x in terms of y.
So, you should find that x = n(n+1)/2 and y = 25n -1. Eliminate n from these two equations to get x in terms of y.
However, I might have misunderstood what you are asking!
+33654 Is the first line meant to be the x-values and the second line the y-values? (Actually, the values in each line are sequential, though not with a constant interval in the case of the first line.)
If so, I suggest you first use your method of differences on each line separately to find x in terms of n (the position number of the items : for n = 1, 2, 3, 4 etc x = 1, 3, 6, 10, etc.
Then eliminate n from the two equations to get x in terms of y.
So, you should find that x = n(n+1)/2 and y = 25n -1. Eliminate n from these two equations to get x in terms of y.
However, I might have misunderstood what you are asking!
