The Error Analysis For Accelerating Convergence Of Limit Periodic Continued Fraction

Accelerating convergence for limit periodic continued fraction hold the important status in the continued fraction theory.This article first chapter obtained from the continued fraction definition, outlined continued fraction of basic property , forward and backward three recurrence formulas in detail, brief introductioned continued fraction equivalence transformation and several kind of special continued fraction forms finally.Accelerating convergence for continued fraction relates with its convergence, this article second chapter introduced together several very classical continued fraction convergence theorem, convergence result of periodic continued fraction, summarized finally related process algorithm with accelerating convergence for continued fraction.The accelerating convergence of continued fraction have the extremely widespread application in the engineering technology domain. This article third chapter introduced with emphasis two methods of the accelerating convergence of continued fraction - - the accelerating convergence factor and the sequence transform method, studied the error of accelerating convergence for limit periodic continued fraction and gave the erroneous expression.