Soumen Pal

activity

20242026

collaborators

4 papers

math.DS2026

Relaxed Newton's Method as a Family of Root-finding Methods: Dynamics and Convergence

Soumen Pal

Relaxed Newton's method is a one-parameter family of root-finding methods that generalizes the classical Newton's method. When viewed as a rational map on the Riemann sphere, this…

math.DS2026

Newton's method applied to rational functions: Fixed points and Julia sets

Tarakanta Nayak, Soumen Pal, Pooja Phogat

For a rational function $R$ , let $N_{R} (z) = z - \frac{R ( z )}{R ^{'} ( z )} .$ Any such $N_{R}$ is referred to as a Newton map. We determine all the rational functions $R$ for which $N_{R}$ has exact…

math.DS2025

On the dynamics of Halley's method

Gang Liu, Soumen Pal, Saminathan Ponnusamy

In this article, we study the global dynamics of Halley's method applied to complex polynomials. Specifically, we analyze the structure and connectivity of the Julia set of this me…

math.DS2024

Chebyshev's method for exponential maps

Subhasis Ghora, Tarakanta Nayak, Soumen Pal +1

It is proved that the Chebyshev's method applied to an entire function $f$ is a rational map if and only if $f (z) = p (z) e^{q (z)}$ , for some polynomials $p$ and $q$ . These are refe…