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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…
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…
Newton's method applied to rational functions: Fixed points and Julia sets
Tarakanta Nayak, Soumen Pal, Pooja Phogat
For a rational function , let Any such is referred to as a Newton map. We determine all the rational functions for which has exact…
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 is a rational map if and only if , for some polynomials and . These are refe…
Julia sets of rational maps with rotational symmetries
Tarakanta Nayak, Soumen Pal
By a symmetry of the Julia set of a polynomial, also referred as polynomial Julia set, we mean an Euclidean isometry preserving the Julia set. Each such symmetry is in fact a rotat…
On dynamics of the Chebyshev's method for quartic polynomials
Tarakanta Nayak, Soumen Pal
Let be a normalized (monic and centered) quartic polynomial with non-trivial symmetry groups. It is already known that if is unicritical, with only two distinct roots with…