Abstract Comparison of two numbers is one of the most frequently used operations, but it
has been a challenging task to efficiently compute the comparison function in homomorphic …

A general family of iterative methods including a free parameter is derived and proved to be
convergent for computing matrix sign function under some restrictions on the parameter …

This work proposes a new scheme under the umbrella of iteration methods to compute the
sign of an invertible matrix. To this target, a review of the exiting solvers of the same type is …

The objective of this study is to extract two pairs of left and right deflating subspaces of a
regular matrix pencil A− λ B corresponding to the eigenvalues lying inside and outside the …

The computation of the sign function of a matrix plays a crucial role in various mathematical
applications. It provides a matrix-valued mapping that determines the sign of each …

In this paper we study random non-autonomous second order linear differential equations
by taking advantage of the powerful theory of random difference equations. The coefficients …

In this paper, we analyze the stability of the family of iterative methods designed by Jarratt
using complex dynamics tools. This allows us to conclude whether the scheme known as …

A new eighth-order Chebyshev-Halley type iteration is proposed for solving nonlinear
equations and matrix sign function. Basins of attraction show that several special cases of …

The security issues that arise in public cloud environments raise several concerns about
privacy-preserving. Conventional security practices successfully protect stored and …

We define and investigate a globally convergent iterative method possessing sixth order of
convergence which is intended to calculate the polar decomposition and the matrix sign …