Solving A Square Root Problem Using the Pierce Continued Fraction

• Author(s): A.C.G. Perera ; K.D.E. Dhananjaya
• Paper ID: 1703837
• Page: 16-22
• Published Date: 04-10-2022
• Published In: Iconic Research And Engineering Journals
• Publisher: IRE Journals
• e-ISSN: 2456-8880
• Volume/Issue: Volume 6 Issue 4 October-2022

Abstract

In this paper, we have developed a new continued fraction using the pierce expansion which is called the pierce continued fraction. There are several applications of continued fractions and one important application is the approximation to the square root problem. In our work, we have introduced new convergent sequences to solve this problem using pierce continued fraction. The convergent rate of these two continued fractions is different from each other. Furthermore, an algorithm was developed using Matlab programmed to find the pierce continued fraction. In future work, we hope to construct a new approach to solve the pelle’s equation.

Keywords

Approximation to the square root problem, continued fraction, convergent, pierce expansion, pierce continued fraction

Citations

IRE Journals:
A.C.G. Perera , K.D.E. Dhananjaya "Solving A Square Root Problem Using the Pierce Continued Fraction" Iconic Research And Engineering Journals Volume 6 Issue 4 2022 Page 16-22

IEEE:
A.C.G. Perera , K.D.E. Dhananjaya "Solving A Square Root Problem Using the Pierce Continued Fraction" Iconic Research And Engineering Journals, 6(4)