Research in mathematics at Cameron University / Samundra Regmi, Ioannis K. Argyros, Janak Joshi and Parshuram Budhathoki, editors. [electronic resource]

Includes bibliographies and index.

The history of Newton's method and extended classical results -- Extended global convergence of iterative methods -- Extended Gauss-Newton-approximate projection methods of constrained nonlinear least squares problems -- Convergence analysis of inexact Gauss-Newton like for solving systems -- Local convergence of the Gauss-Newton scheme on Hilbert spaces under a restricted convergence domain -- Ball convergence for inexact Newton-type conditional gradient solver for constrained systems -- Newton-like methods with recursive approximate inverses -- Updated mesh independence principle -- Ball convergence for ten solvers under the same set of conditions -- Extended Newton's solver for generalized equations using a restricted convergence domain -- Extended Newton's method for solving generalized equations : Kantorovich's approach -- Extended robust convergence analysis of Newton's method for cone inclusion problems in Banach spaces -- Extended and robust Kantorovich's theorem on the inexact Newton's method with relative residual error tolerance -- Extended local convergence for iterative schemes using the gauge function theory -- Improved local convergence of inexact Newton methods under average Lipschitz-type conditions -- Semi-local convergence of Newton's method using the gauge function theory : an extension -- Extending the semi-local convergence of Newton's method using the gauge theory -- Global convergence for Chebyshev's method -- Extended convergence of efficient King-Werner-type methods of order 1+ [square root of 2. -- Extended convergence for two Chebyshev-like methods -- Extended convergence theory for Newton-like methods of bounded deterioration -- Extending the Kantorovich theorem for solving equations using telescopic series -- Extended [omega]-convergence conditions for the Newton-Kantorovich method -- Extended semilocal convergence analysis for directional Newton method -- Extended convergence of damped Newton's method -- Extended convergence analysis of a one-step intermediate Newton iterative scheme for nonlinear equations -- Enlarging the convergence domain of secant-type methods -- Two-step Newton-type method for solving equations -- Two-step secant-type method for solving equations -- Unified convergence for general iterative schemes -- Extending the applicability of Gauss-Newton method for convex composite optimization -- Local convergence comparison between Newton's and the secant method : part-I -- Convergence comparison between Newton's and secant method : part-II -- Extended convergence domains for a certain class of Fredholm-Hammerstein equations -- Extended convergence of the Gauss-Newton-Kurchatov method -- Extended semi-local convergence of Newton's method under conditions on the second derivative -- Extended convergence for the secant method under Mysovskii-like conditions.

"Numerous 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 iterative algorithms, which seem to be the only alternative. Due to the explosion of technology, faster and faster computers become available. This development simply means that new optimized algorithms should be developed to take advantage of these improvements. That is exactly where we come in with our book containing such algorithms with applications in problems from numerical analysis and economics but also from other areas such as biology, chemistry, physics, parallel computing, and engineering. The book is an outgrowth of scientific research conducted over two years. This book can be used by senior undergraduate students, graduate students, researchers, and practitioners in the aforementioned areas in the classroom or as 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 readers"--

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