Cycles and Convergence

• If a cell depends on itself, that forms a cycle

• Spreadsheet may not converge when evaluated

• Can be used to implement iterative algorithms

Example: Newton's method to find the square root of x:

x = 2;  a0 = b0 ? b0 : x/2;  b0 = (a0+x/a0)/2;

Since a0 depends on b0, and b0 depends on a0, there is a cycle.

Newton's method converges quickly:

ss_eval: converged after 7 iterations

    A                    B
0   1.41421356237309492  1.41421356237309492