A New Approach to Find Non-simple Zero’s of Functions

Mohsen Jamali, Mehdi Delkhosh


Finding acceptable approximation of zeros of even multiplicity of functions by the prevalent method of numerical analysis is impossible or difficult. In this paper we introduce the Intersecting Lines Method and its modified version applying to approximate zeros of even multiplicity of functions. We apply this method to approximate relative extremum points of differentiable functions.


Convex function, zero of even multiplicity of function, Newton-Raphson method, relative extrema of function

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Ralston A. and Rabinowitz P., First

Course in Numerical Analysis, McGraw-

Hill, New York, 1978.

TRAUB J.F., Iterative Methods for the

Solution of Equations, Prentice Hall,

Englewood Cliffs, N.J., 1964.

Stoer J., and Bulirsch R., Introduction to

Numerical Analysis, Third Edition,

Springer, New York, 2002.

Brent R.P., Algorithms for Minimization

without Derivatives, Prentice Hall,

Englewood Cliffs, N.J., 1973.

Yakoubsohn J.C., Numerical analysis of a

bisection-exclusion method to find zeros

of univariate analytic functions, Journal of

Complexity 2005, Vol. 21, Issue 5, p. 652–

Segura J., the Zeros of Special Functions from a Fixed Point Method, SIAM J. Numer. Anal. 2002, Vol. 40(1), pp. 114–133.

Meylan M.H., Gross L., A parallel algorithm to find the zeros of a complex analytic function, ANZIAM Journal 2003, 44(E), p. E236–E254.


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