1. A method implemented on at least one computing system of determining convergence of a rank, the at least one computing system including at least one processor, the method comprising: receiving the rank, the received rank being an output of a first computation; determining an estimated input of a second computation based on the received rank, the received rank being a converged solution of the second computation resulting from the estimated input; comparing the estimated input of the second computation to a predetermined input; identifying a termination point of convergence based on the comparison, the point of convergence corresponding to a rank of an output of a web page search; and determining whether a convergence condition is met based on the estimated input and the predetermined input, wherein if the convergence condition is not met, receiving a subsequent rank, determining a subsequent estimated input of the second computation based on the subsequent rank, and determining whether the convergence condition is met based on the predetermined input and the subsequent estimated input.