On the p-adic analogue of the Newton-Raphson method for finding the zero of a polynomial
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 o...
| Main Author: | |
|---|---|
| Other Authors: | |
| Resource Type: | Thesis |
| Language: | English |
| Published: |
Quezon City
Institute of Mathematics, College of Science, University of the Philippines Diliman
2015.
|
| Subjects: |
| Summary: | 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. |
|---|---|
| Physical Description: | viii, 49 leaves c28cm |
| Access: | 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. |