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 Ball Convergence of Iterative Methods without Derivatives with or without Memory Relying on the Weight Operator Technique(CRC Press, 2023) Argyros, I.K.; George, S.; Argyros, C.A method without memory as well as a method with memory are developed free of derivatives for solving Banach space valued equations. Their ball convergence analysis is provided using only the derivative and the divided difference of order one in contrast to earlier works on the real line using the fifth as well as the seventh derivative. This way the applicability is expanded for these methods. © 2024 selection and editorial matter, Pradip Debnath, Delfim F.M. Torres, Yeol Je Cho; individual chapters, the contributors.Item Gauss-newton methods for convex composite optimization under generalized continuity conditions(CRC Press, 2024) Argyros, I.K.; George, S.; Argyros, M.I.[No abstract available]Item A Class of Frozen Regularized Gauss-Newton Methods Under Weak Conditions(Springer, 2025) George, S.; Jidesh, P.Qinian Jin (2010) studied Frozen Regularized Gauss Newton Method (FRGNM) for approximating a solution of nonlinear ill-posed equation. The assumptions used to prove results in Jin’s paper are too restrictive. In this study, we analyze the convergence of FRGNM under weaker assumptions. This way we extend the applicability of FRGNM to the problems which does not satisfy the assumptions in Qinian Jin (2010). We also provide numerical results obtained for five different parameter choice strategies for FRCNM. © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2025.Item Ball Convergence of a Fifth-Order Method for Solving Equations Under Weak Conditions(Springer, 2021) Argyros, I.K.; George, S.; Erappa, S.M.We develop a ball convergence for a fifth-order method to find a solution for an equation. Earlier studies used conditions on the sixth derivative not present in the methods. Moreover, no error estimates are provided. That is why we used conditions up to the second derivative. Numerical experiments validate the theoretical results. © 2021, The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd.Item Ball Convergence of Multipoint Methods for Non-linear Systems(Springer Science and Business Media Deutschland GmbH, 2021) Argyros, I.K.; George, S.; Erappa, S.M.We study Multipoint methods using only the first derivative. Earlier studies use higher than three order derivatives not on the methods. Moreover Lipschitz constants are used to find error estimates not presented in earlier papers. Numerical examples complete this paper. © 2021, Springer Nature Singapore Pte Ltd.Item Extending the applicability of the inexact Newton-HSS method for solving large systems of nonlinear equations(Springer, 2020) Argyros, I.K.; George, S.; Senapati, K.We revisit the study of the semi-local convergence of the inexact Newton-HSS method (INHSS) introduced by Amiri et al. (2018), for solving large systems of nonlinear equations. In particular, first we present the correct convergence criterion, since the one in the preceding reference is incorrect. Secondly, we present an even weaker convergence criterion using our idea of recurrent functions. Moreover, the bound functions are compared. Finally, numerical examples are provided to show that the earlier convergence criteria are not satisfied but the new ones are satisfied. Hence, the applicability of the INHSS method is extended and under the same information as in the earlier studies. © 2019, Springer Science+Business Media, LLC, part of Springer Nature.