Catalogue Search | MBRL
Are you sure you want to remove the book from the shelf?
{{itemTitle}}
79,036
result(s) for
"Newton"
Sort by:
Newton and the origin of civilization
Isaac Newton'sChronology of Ancient Kingdoms Amended, published in 1728, one year after the great man's death, unleashed a storm of controversy. And for good reason. The book presents a drastically revised timeline for ancient civilizations, contracting Greek history by five hundred years and Egypt's by a millennium.Newton and the Origin of Civilizationtells the story of how one of the most celebrated figures in the history of mathematics, optics, and mechanics came to apply his unique ways of thinking to problems of history, theology, and mythology, and of how his radical ideas produced an uproar that reverberated in Europe's learned circles throughout the eighteenth century and beyond.
Jed Buchwald and Mordechai Feingold reveal the manner in which Newton strove for nearly half a century to rectify universal history by reading ancient texts through the lens of astronomy, and to create a tight theoretical system for interpreting the evolution of civilization on the basis of population dynamics. It was during Newton's earliest years at Cambridge that he developed the core of his singular method for generating and working with trustworthy knowledge, which he applied to his study of the past with the same rigor he brought to his work in physics and mathematics. Drawing extensively on Newton's unpublished papers and a host of other primary sources, Buchwald and Feingold reconcile Isaac Newton the rational scientist with Newton the natural philosopher, alchemist, theologian, and chronologist of ancient history.
eBook
Isaac Newton and the Study of Chronology
Isaac Newton (1642-1727) is best known for his natural philosophical and mathematical works. Yet he devoted ample time to the study of ancient chronology, resulting in the posthumously published The Chronology of Ancient Kingdoms Amended (1728). Here, Newton attempted to show how the antiquity of Greece, Egypt, Assyria, Persia, and other Mediterranean nations could be reinterpreted to fit the timespan allowed for by Scripture. As the hundreds of books from his library and the thousands of manuscript pages devoted to the topic show, the Chronology was long in the making. This volume provides the first comprehensive analysis of the genesis and evolution of Newton's studies of ancient history and demonstrates how these emerged from that other major scholarly project of his, the interpretation of the apocalyptic prophecies in Scripture. A careful study of Newton's reading, note-taking, writing, and ordering practices provides the key to unravelling and reconstructing the chronology of Newton's chronological studies, bringing to light writings hitherto hidden in the archives.
eBook
The Levenberg–Marquardt method: an overview of modern convergence theories and more
The Levenberg–Marquardt method is a fundamental regularization technique for the Newton method applied to nonlinear equations, possibly constrained, and possibly with singular or even nonisolated solutions. We review the literature on the subject, in particular relating to each other various convergence frameworks and results. In this process, the analysis is performed from a unified perspective, and some new results are obtained as well. We discuss smooth and piecewise smooth equations, inexact solution of subproblems, and globalization techniques. Attention is also paid to the LP-Newton method, because of its relations to the Levenberg–Marquardt method.
Journal Article
Inexact proximal DC Newton-type method for nonconvex composite functions
We consider a class of difference-of-convex (DC) optimization problems where the objective function is the sum of a smooth function and a possibly nonsmooth DC function. The application of proximal DC algorithms to address this problem class is well-known. In this paper, we combine a proximal DC algorithm with an inexact proximal Newton-type method to propose an inexact proximal DC Newton-type method. We demonstrate global convergence properties of the proposed method. In addition, we give a memoryless quasi-Newton matrix for scaled proximal mappings and consider a two-dimensional system of semi-smooth equations that arise in calculating scaled proximal mappings. To efficiently obtain the scaled proximal mappings, we adopt a semi-smooth Newton method to inexactly solve the system. Finally, we present some numerical experiments to investigate the efficiency of the proposed method, which show that the proposed method outperforms existing methods.
Journal Article
Optimization algorithms on matrix manifolds
Many problems in the sciences and engineering can be rephrased as optimization problems on matrix search spaces endowed with a so-called manifold structure. This book shows how to exploit the special structure of such problems to develop efficient numerical algorithms. It places careful emphasis on both the numerical formulation of the algorithm and its differential geometric abstraction--illustrating how good algorithms draw equally from the insights of differential geometry, optimization, and numerical analysis. Two more theoretical chapters provide readers with the background in differential geometry necessary to algorithmic development. In the other chapters, several well-known optimization methods such as steepest descent and conjugate gradients are generalized to abstract manifolds. The book provides a generic development of each of these methods, building upon the material of the geometric chapters. It then guides readers through the calculations that turn these geometrically formulated methods into concrete numerical algorithms. The state-of-the-art algorithms given as examples are competitive with the best existing algorithms for a selection of eigenspace problems in numerical linear algebra.
eBook