00000ctm a22000004i 4500 UP-99796217612730931 Buklod 20230214151625.0 m |o d | ta 180413s xx d r |||| u| (iLib)UPD-00362012259 DARCHIVES rda eng DMLUC LG 995 2015 M38 A23 Aban, Janus C. author. On the p-adic analogue of the Newton-Raphson method for finding the zero of a polynomial Janus C. Abad ; Julius M. Basilla, adviser. Quezon City Institute of Mathematics, College of Science, University of the Philippines Diliman 2015. viii, 49 leaves c28cm text rdacontent unmediated rdamedia volume rdacarrier Thesis (Master of Science in Mathematics)--University of the Philippines Diliman June2015. P- the author wishes to publish the work personally Yes-Available to the general public. No-Available only after consultation with author/adviser for thesis. No-Available only to those bound by non-disclosure or confidentiality agreement. Hensel's Lemma is a very powerful tool in determining the existence of a root of polynomials contained in zp(x). It is just the p-adic analog of the Newton-Raphson root-finding algorithm from Numerical Analysis. In this thesis we extend the Hensel's Lemma to a bigger class of polynomials over arbitrary complete field K with non-Archimidean norm induced by principal valuation. For K = Qp the p-adic numbers, we give some type of polynemials covered by the extension of Hansel's Lemma. Then for the polynomial of the form f(x) = x - a E Qp(x) where q is an abritrary natural number we determine the sufficident conditions so that the Newton-Raphson method will work. For the computational part we calculate the order of the speed of convergence of the sequence obtained from the Newton-Raphson iterations converging to a root of polynomial f(x) = xq - a. We also determine the number of iterations needed to obtain a desired number of correct digits in the approximate of qth root of a. Newton-Raphson method. Algebra. Analogy (Mathematics). Basilla, Julius M. thesis adviser. Thesis FI UP UPD DARCHIVES LG 995 2015 M38 A23 Thesis