Using Golden Section Search in Excel

Step 1) (Because I had no idea what the "golden search" algorithm even looked like) was to look it up to understand the mathematics/generic algorithm: http://en.wikipedia.org/wiki/Golden_section_search My first observation was that this is essentially the same as the bisection root finding algorithm, only the calculation of x3 from x1 and x2 is a little different. Not sure what the advantage would be of choosing x3 based on these ratios rather than the midpoint of x1 and x2, but I'm sure there is some reason. If your question is less about Excel and more about how the golden section search algorithm works, I would probably suggest that you start with the Wikipedia page or other tutorial.

2) Preliminary concepts: Since this is so similar to the bisection algorithm, if you have previously been introduced and have a spreadsheet for that algorithm, I would probably use that as your starting point for this algorithm. If you are at all unfamiliar with the use of relative and absolute references in a spreadsheet, then I would search some basic spreadsheet tutorials to become familiar with that concept. This is a key concept for an algorithm like this, because a spreadsheet solution for this will make heavy use of "copy and paste" operations, and you will need to be familiar with how cell references change with the copy and paste operation.

3) I would start a spreadsheet like this by blocking off 4 groups of columns (maybe 10 columns each, depending on how many cells I think I need for each calculation of f(x) from each input x value). Each row will contain the 4 sets of calculations needed for a single iteration.
a) in the left group of columns, I would enter my initial x1 and compute f(x1). Pay close attention to your relative and absolute references during this step, because this 1 row by 10 block of cells becomes the heart of the entire spreadsheet. Program this block of cells correctly, and the rest of the spreadsheet is mostly copies of this block of cells.
b) Take 3a and copy it into the 2nd group of columns, then enter your desired value for x2. If you did 3a right, f(x2) should calculate automatically.
c) Take 3a and copy it into the 3rd group of column, then enter a formula for x3 that will look at x1 and x2 and calculate the desired value for x3 (see the wikipedia article if you are unsure what this formula should be). Again, if you did 3a correctly, f(x3) should compute automatically.
d) copy 3a into the 4th group of columns, and enter a formula for x4 based on x3 and x2.
e) at the end of each row structure a block of cells that will test for convergence. I also like to have a few cell at the end of the row that will look at all of these values and determine if the next x1 value should be the same as the old x1 value or if it should be the x3 value. Same for new x2.
4) Copy the row created in step 3 and paste into the next row. Adjust the formulas for x1 and x2 in this row to look at the previous row for these values. If you have done this right (with the correct combination of relative and absolute references), then this entire row should update with new x3,f(x3) = x4, f(x4) = and determine new values for x1 and x2.
5) Take the row from step 4 and copy it down 20 or 40 or however many rows/iterations you think you need. If you have everything correctly so far, this should be all that is needed (except maybe a step to show the actual result).

That's an overall look at the algorithm. If you need specific help with individual steps, let us know.