The Study Of Truncation Error Estimate Of Limit Periodic Continued Fraction

Continued fraction is an important nonlinear numerical analytic method innumerical approximation field. With wide application in engineering technology, ithas become a distinctive system after four-hundred yeas development. Acceleratingconvergence holds an important status in continued fraction theory, and the study ofit has greatly developed in the past half decade. Referring to the popular method ofsequence transformation and choices of accelerating convergence factors, peoplekeep on researching new accelerating method, introducing new conclusionsalgorithm into the study of the present problems. As a result, the prolongation ofnew angle of view leads to the development of continued fraction.Limit periodic continued fraction is a special continued fraction, and plays animportant role in analytic theory of continued fraction. In the past thirty years,many researchers in the word has focused their study on the limit periodiccontinued fraction, and obtained a variety of results.In this paper, further work is done based on the present results for limitperiodic continued fraction with the form of (α_n/1). Firstly, we introduce somedefinitions and basic concepts about continued fraction. Secondly, importantconvergence and accelerating convergence theorems and new methods ofDrummond transformation are given for accelerating the convergence of limitperiodic continued fraction. Furthermore, for a kind of limit periodic continuedfraction with the condition α_n≤1/4, smaller truncation error bound is obtained bythe backward recurrence relation, and its application in accelerating convergence isalso studied.