A NEW CONTINUED FRACTION ALGORITHM AND ITS CONVERGENCE
一个新的连分式算法及其收敛性

This paper proposes a new linear search method: the continued fraction algorithm. It re-quires computing only three functional values at each iteration, and using one division in com-puting every coefficient of the continued fraction interpolation. Its numerical stability is good,and its convergence rate is fast. The order of convergence is approximately 1.8393. Thus, thisalgorithm is a very attractive method for the local one-dimensional optimization. If we usethis method for the imprecise linear search, it is necessary only to compute three functional va-lues. It can also be applied to solve the transcendental equation.