Home  18.013A  Chapter 12 


How can you do such things?
First put x and j in fixed locations X and Y.
Then set up the following columns on the spreadsheet:
f(x_{j}):
In the first column enter the successive values of f(x_{j}) starting with the first, known value.
For roots you can start with x_{0} = f(x_{0}) = 1.
Compute later values f(x_{j}) by using the linear approximation tangent line at x_{j1} evaluated at argument x, fLx_{j1}(x) or f(x_{j1}) + f '(x_{j1}) (xx_{j1}). (x_{j1} is the entry in the second column in the previous row.)
x_{j}:
In the second column apply the inverse function, f ^{1} to the value in the first column.
Once you have entered your instructions for f(x_{1}) and x_{1}, you can copy these down a hundred rows, and you are done.
What happens if f is a root, x^{1/m}?
In general we have
f(x_{j}) = fLx_{j1}(x) = f(x_{j1}) + (x  x_{j1})f '(x_{j1})
For jth root, so that this formula reduces to
And that is all you need enter. The rest is copying down.
