An Efficient Method for the Limit Estimation of Slowly Convergent Sequence of Numbers.

Advances made in electronic computers allows the limit value of the sequence to be determined much more easily now than in the past. However, a problem still arises frequently in which it is difficult to determine the limit value with a high accuracy when a tremendous calculation is required in the determination of each term of the sequence. This paper proposes a theoretical method to estimate the limit value of the sequence with a high accuracy from the viewpoint of the recognition theory. By examining the gradual change of the sequence, the character inherent to the sequence is derived. By utilizing the character, the limit value can be estimated with a high accuracy directly from a small number of terms of the sequence. Lastly, the effectiveness of the proposed estimation method is demonstrated by simple examples. [ABSTRACT FROM AUTHOR]