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New Methods for Finding the nth Root of a Number

Nitin A Jain1, Kushal D Murthy1, Dr. Hamsapriye2
  1. Student, Department of Electronics & Communication Engineering, R.V. College of Engineering, Bangalore, Karnataka, India
  2. Professor, Department of Mathematics, R.V. College of Engineering, Bangalore, Karnataka, India
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Abstract

New methods for finding the nth root of a positive number m, to any degree of accuracy, are discussed. These methods are based on finding eigen values and eigen vectors of a special matrix. For even order matrices, the method is founded on the well-known power method. The desired root and its higher powers can also be obtained from the same matrix.

Keywords

Iterative algorithm, Diagonalization, Power method, Dominant Eigen Value.

AMS Classification

65D99

I. INTRODUCTION

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Therefore, the successive generation of the sequence of approximations to ��, involve the multiplication of higher powers of the square matrix in (3). The convergence of the iterative algorithm directly depends on the nature of the eigen values and eigen vectors of the matrix.
Based on linear algebra concepts, [3] generealizes and mathematically proves the matrix method of [2]. This generalized form of the square matrix in (3) is given to be
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References

[1] Kendall E. Atkinson, “An Introduction to Numerical Analysis”, John Wiley & Sons, Second Edition 1988.

[2] Theodore Eisenberg, “On an unknown algorithm for computing square roots”, International Journal for Mathathematical Education in Science and Technology, 34 (1), pp. 153 - 158, 2003.

[3] Nitin A Jain, Kushal D Murthy and Hamsapriye, “Matrix methods for finding n mu”, International Journal for Mathathematical Education in Science and Technology, 45(2), pp. 1 - 9, 2014.

[4] Nitin A Jain, Kushal D Murthy and Hamsapriye, “On Finding the n mu leading to Newton-Raphson's Improved method”, Accepted for publication in International Journal of Emerging Technologies in Computational and Applied Sciences, Issue 9, June - August, 2014.