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The Newton-Raphson method is used to compute the q-th roots of a p-adic number for a prime number q. The sufficient conditions for the convergence of this method are obtained. The speed of its convergence and the number of iterations to obtain a number of corrected digits in the approximation are calculated.
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참고문헌 (10)
참고문헌 신청
W. Cheney / 2007 / Numerical mathematics and computing / Thomson
P. S. Ignacio / 2013 / On the square and cube roots of p-adic numbers / J. Math. Comput. Sci 3(4):993~1003
P. S. Ignacio / 2013 / Computation of square and cube roots of p-adic numbers via Newton-Raphson method / J. Math. Research 5(2):31~38
S. Katok / 2007 / p-Adic analysis compared with real
M. Keicies / 2013 / General approach of the root of a p-adic number / Filomat 27(3):431~436
P. S. Ignacio / 2013 / On the square and cube roots of p-adic numbers / J. Math. Comput. Sci 3(4):993~1003
P. S. Ignacio / 2013 / Computation of square and cube roots of p-adic numbers via Newton-Raphson method / J. Math. Research 5(2):31~38
S. Katok / 2007 / p-Adic analysis compared with real
M. Keicies / 2013 / General approach of the root of a p-adic number / Filomat 27(3):431~436
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