Search results for ""Author Ioannis K Argyros""

Numerous problems from diverse disciplines can be converted using mathematical modelling 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 seems to be the only alternative. Due to the explosion of technology, scientific and parallel computing, faster and faster computers become available. This development simply means that new optimized algorithms should be developed to take advantage of these improvements. There is exactly where we come in with our book containing such algorithms with application especially in problems from Economics but also from other areas such as Mathematical: Biology, Chemistry, Physics, Scientific, Parallel Computing, and also Engineering. The book can be used by senior undergraduate students, graduate students, researchers and practitioners in the aforementioned area 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.

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The exponential growth of technology forces all disciplines to adjust accordingly, so they can meet the demands of a very dynamic world that heavily depends upon it. Therefore, mathematics cannot be an exception. In fact, mathematics should be the first to adjust and in fact it is. In this volume, which is a continuation of the previous three under the same title, we present state-of-the-art iterative methods for solving equations related to concrete problems from diverse areas such as applied mathematics, mathematical: biology, chemistry, economics, physics and also engineering to mention a few. Most of these methods are new and a few are old but still very popular. One major problem with iterative methods is that the convergence domain is small in general. We have introduced a technique that finds a smaller set than before containing the iterates leading to tighter Lipschitz functions than before. This way and under the same computational effort, we derive: weaker sufficient convergence criteria (leading to a wider choice of initial points); tighter error bounds on the distances involved (i.e., fewer iterates are needed to obtain a desired predetermined accuracy), and a more precise information on the location of the solution. These advantages are considered major achievements in computational disciplines. The volume requires knowledge of linear algebra, numerical functional analysis and familiarity with contemporary computing programing. It can be used by researchers, practitioners, senior undergraduate and graduate students as a source material or as a required textbook in the classroom.

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This book is intended for undergraduate and graduate researchers and practitioners in computational sciences and as a reference book for an advanced computational methods course. We have included new results for iterative procedures in abstract spaces general enough for handling inverse problems in various situations related to real-life problems through mathematical modeling. The book contains a plethora of updated bibliography and provides comparison between various investigations made in recent years in the field of computational mathematics in the wide sense. Iterative processes are the tools used to generate sequences approximating solutions of equations describing the real-life problems stated above and others originating from Biosciences, Engineering, Mathematical Economics, Mathematical Biology, Mathematical Chemistry, Mathematical Physics Medicine, Mathematical Programming, and other disciplines. The book also provides recent advancements on the study of iterative procedures and can be used as a source from which one can obtain the proper method to use in order to solve a problem. The book requires a fundamental background in Mathematical Statistics, Linear Algebra and Numerical Analysis. It may be used as a self-study reference or as a supplementary text for an advanced course in Biosciences, Engineering and Computational Sciences.

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These books are intended for undergraduate, graduate researchers and practitioners in computational sciences, and as reference books for an advanced computational methods course. We have included new results for iterative procedures in abstract spaces general enough for handling inverse problems in various situations related to real life problems through mathematical modeling. These books contain a plethora of updated bibliography and provide comparison between various investigations made in recent years in the field of computational mathematics in the wide sense. Iterative processes are the tools used to generate sequences approximating solutions of equations describing the real life problems stated above and others originating from biosciences, engineering, mathematical economics, mathematical biology, mathematical chemistry, mathematical physics medicine, mathematical programming, and other disciplines. These books also provide, recent advancements on the study of iterative procedures, and can be used as a source from which one can obtain the proper method to use in order to solve a problem. The books require a fundamental background in mathematical statistics, linear algebra and numerical analysis. It may be used as a self-study reference or as a supplementary text for an advanced course in biosciences, engineering and computational sciences.

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Researchers are faced with the problem of solving a variety of equations in the course of their work in engineering, economics, physics, and the computational sciences. This book focuses on a new and improved local-semilocal and monotone convergence analysis of efficient numerical methods for computing approximate solutions of such equations, under weaker hypotheses than in other works. This particular feature is the main strength of the book when compared with others already in the literature.The explanations and applications in the book are detailed enough to capture the interest of curious readers and complete enough to provide the necessary background material to go further into the subject.

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