Faculty Publications
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Item Contemporary Algorithms: Theory and Applications. Volume I(Nova Science Publishers, Inc., 2022) Argyros, C.; Regmi, S.; Argyros, I.K.; George, S.This book provides different avenues to study algorithms. It also brings new techniques and methodologies to problem solving in computational sciences, engineering, scientific computing and medicine (imaging, radiation therapy) to mention a few. A plethora of algorithms which are universally applicable are presented in a sound, analytical way. The chapters are written independently of each other, so they can be understood without reading earlier chapters. But some knowledge of analysis, linear algebra, and some computing experience is required. The organization and content of this book cater to senior undergraduate, graduate students, researchers, practitioners, professionals, and academicians in the aforementioned disciplines. It can also be used as a reference book and includes numerous references and open problems. © 2022 by Nova Science Publishers, Inc. All rights reserved.Item Contemporary Algorithms: Theory and Applications, Volume V(Nova Science Publishers, Inc., 2025) Argyros, M.I.; Regmi, S.; Argyros, I.K.; George, S.Due to the explosion of technology as well as scientific and parallel computing, faster computers have become available. This development simply means that new optimization algorithms should be introduced to take advantage of these developments. This book provides different avenues for studying algorithms. It also brings new techniques and methodologies to problem solving in Computational Sciences, Engineering, Scientific Computing and Medicine (imaging, radiation therapy). 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, Hilbert space, Banach Space or even more general spaces. The solution to these equations is sought in a closed form. But this is only possible in special cases. That is why researchers and practitioners must use algorithms as an alternative. © 2025 by Nova Science Publishers, Inc.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 Contemporary algorithms: Theory and applications(Nova Science Publishers, Inc., 2023) Argyros, C.I.; Regmi, S.; Argyros, I.K.; George, S.The book provides different avenues to study algorithms. It also brings new techniques and methodologies to problem solving in computational Sciences, Engineering, Scientific Computing and Medicine (imaging, radiation therapy) to mention a few. A plethora of algorithms which are universally applicable is presented on a sound analytical way. The chapters are written independently of each other, so they can be understood without reading earlier chapters. But some knowledge of Analysis, Linear Algebra and some Computing experience is required. The organization and content of the book cater to senior undergraduate, graduate students, researchers, practitioners, professionals and academicians in the aforementioned disciplines. It can also be used as a reference book and includes numerous references and open problems. © 2023 by Nova Science Publishers, Inc. All rights reserved.Item Local comparison between two ninth convergence order algorithms for equations(MDPI AG rasetti@mdpi.com Postfach Basel CH-4005, 2020) Regmi, S.; Argyros, I.K.; George, S.A local convergence comparison is presented between two ninth order algorithms for solving nonlinear equations. In earlier studies derivatives not appearing on the algorithms up to the 10th order were utilized to show convergence. Moreover, no error estimates, radius of convergence or results on the uniqueness of the solution that can be computed were given. The novelty of our study is that we address all these concerns by using only the first derivative which actually appears on these algorithms. That is how to extend the applicability of these algorithms. Our technique provides a direct comparison between these algorithms under the same set of convergence criteria. This technique can be used on other algorithms. Numerical experiments are utilized to test the convergence criteria. © 2020 by the authors.Item Direct comparison between two third convergence order schemes for solving equations(MDPI AG, 2020) Regmi, S.; Argyros, I.K.; George, S.We provide a comparison between two schemes for solving equations on Banach space. A comparison between same convergence order schemes has been given using numerical examples which can go in favor of either scheme. However, we do not know in advance and under the same set of conditions which scheme has the largest ball of convergence, tighter error bounds or best information on the location of the solution. We present a technique that allows us to achieve this objective. Numerical examples are also given to further justify the theoretical results. Our technique can be used to compare other schemes of the same convergence order. © 2020 by the authors. Licensee MDPI, Basel, Switzerland.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.Item On the local convergence and comparison between two novel eighth convergence order schemes for solving nonlinear equations(Cambridge Scientific Publishers, 2021) Regmi, S.; Argyros, I.K.; George, S.; Argyros, C.I.We compare two eighth order schemes for solving nonlinear equations involving Banach space valued equations. This is done by using assumptions only on the first derivative that does appear on the schemes, whereas in earlier works up to the ninth derivative (not on the scheme) are used to establish the convergence. Our technique is so general that it can be used to extend the usage of other schemes along the same lines. © 2021. All Rights Reserved.Item Extended kung–traub methods for solving equations with applications(MDPI, 2021) Regmi, S.; Argyros, I.K.; George, S.; Magreñán Ruiz, Á.A.; Argyros, M.Kung and Traub (1974) proposed an iterative method for solving equations defined on the real line. The convergence order four was shown using Taylor expansions, requiring the existence of the fifth derivative not in this method. However, these hypotheses limit the utilization of it to functions that are at least five times differentiable, although the methods may converge. As far as we know, no semi-local convergence has been given in this setting. Our goal is to extend the applicability of this method in both the local and semi-local convergence case and in the more general setting of Banach space valued operators. Moreover, we use our idea of recurrent functions and conditions only on the first derivative and divided difference, which appear in the method. This idea can be used to extend other high convergence multipoint and multistep methods. Numerical experiments testing the convergence criteria complement this study. © 2021 by the authors. Licensee MDPI, Basel, Switzerland.