Faculty Publications
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Item Contemporary algorithms: Theory and applications. Volume IV(Nova Science Publishers, Inc., 2024) Argyros, G.I.; Regmi, S.; Argyros, I.K.; George, S.Due to the explosion of technology, scientific and parallel computing, faster computers have become available. This development simply means that new optimized algorithms should be developed to take advantage of these improvements. There is where this book containing such algorithms comes in handy, with applications in economics, mathematics, biology, chemistry, physics, parallel computing, engineering, and also numerical solution of differential and integral equations. A plethora of problems from diverse disciplines can be converted using mathematical modeling to an equation defined on suitable abstract spaces usually involving the n-dimensional Euclidean space or Hilbert space or Banach Space or even more general spaces. The solution of these equations is sought in closed form. But this is possible only in special cases. That is why researchers and practitioners use algorithms which seem to be the only alternative. This book can be used by senior undergraduate students, graduate students, researchers and practitioners in the aforementioned areas in the classroom or as a reference material. Readers should know the fundamentals of numerical functional analysis, economic theory, and Newtonian physics. Some knowledge of computers and contemporary programming shall be very helpful to the readers. © 2024 by Nova Science Publishers, Inc. All rights reserved.Item On the solution of equations by extended discretization(MDPI Multidisciplinary Digital Publishing Institute rasetti@mdpi.com, 2020) Argyros, G.I.; Argyros, M.I.; Regmi, S.; Argyros, I.K.; George, S.The method of discretization is used to solve nonlinear equations involving Banach space valued operators using Lipschitz or Hölder constants. But these constants cannot always be found. That is why we present results using ?- continuity conditions on the Fréchet derivative of the operator involved. This way, we extend the applicability of the discretization technique. It turns out that if we specialize ?- continuity our new results improve those in the literature too in the case of Lipschitz or Hölder continuity. Our analysis includes tighter upper error bounds on the distances involved. © 2020 by the authors.Item Extending the applicability of newton’s algorithm with projections for solving generalized equations(MDPI AG diversity@mdpi.com, 2020) Argyros, M.I.; Argyros, G.I.; Argyros, I.K.; Regmi, S.; George, S.A new technique is developed to extend the convergence ball of Newton’s algorithm with projections for solving generalized equations with constraints on the multidimensional Euclidean space. This goal is achieved by locating a more precise region than in earlier studies containing the solution on which the Lipschitz constants are smaller than the ones used in previous studies. These advances are obtained without additional conditions. This technique can be used to extend the usage of other iterative algorithms. Numerical experiments are used to demonstrate the superiority of the new results. © 2020 by the authors. Licensee MDPI, Basel, Switzerland.