S-iteration scheme and polynomiography

Strong Convergence for Hybrid S-Iteration Scheme

Alternating Sign Matrices and Polynomiography

To each permutation matrix we associate a complex permutation polynomial with roots at lattice points corresponding to the position of the ones. More generally, to an alternating sign matrix (ASM) we associate a complex alternating sign polynomial. On the one hand visualization of these polynomials through polynomiography, in a combinatorial fashion, provides for a rich source of algorithmic ar...

Perturbation Mappings in Polynomiography

In the paper, a modification of rendering algorithm of polynomiograph is presented. Polynomiography is a method of visualization of complex polynomial root finding process and it has applications among other things in aesthetic pattern generation. The proposed modification is based on a perturbation mapping, which is added in the iteration process of the root finding method. The use of the pert...

A Cyclic Douglas-Rachford Iteration Scheme

In this paper we present two Douglas–Rachford inspired iteration schemes which can be applied directly to N-set convex feasibility problems in Hilbert space. Our main results are weak convergence of the methods to a point whose nearest point projections onto each of the N sets coincide. For affine subspaces, convergence is in norm. Initial results from numerical experiments, comparing our metho...

Newton-Ellipsoid Method and its Polynomiography

We introduce a new iterative root-finding method for complex polynomials, dubbed Newton-Ellipsoid method. It is inspired by the Ellipsoid method, a classical method in optimization, and a property of Newton’s Method derived in [7], according to which at each complex number a half-space can be found containing a root. Newton-Ellipsoid method combines this property, bounds on zeros, together with...