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. Optimization Algorithms on Matrix Manifolds offers techniques with broad applications in linear algebra, signal processing, data mining, computer vision, and statistical analysis. It can serve as a graduate-level textbook and will be of interest to applied mathematicians, engineers, and computer scientists.
First published in 2007. An encyclopaedic account of traditional Chinese festivals, customs and beliefs, lavishly illustrated with line drawings and paintings, this remarkable work by an Englishman who spent twenty years in China from the Imperial aftermath through the establishment of Communism, gives fascinating insights into a complex culture poised between past and present. Burckhardt's beautifully written and detailed work includes the rites practiced by the Manchu royal court and the rituals permitted under the Communist and Nationalist regimes, the festivals of working people and villagers as well as the ceremonies of the mandarins of Peking and Hong Kong, in all seasons of the year. He was especially close to the renowned Boat People of the former colony, and gives a unique account of life abroad the harbour junks and their sea-borne celebrations. Among the subjects dealt with are Chinese cuisine, the meaning of presents, secret societies, the Chinese calendar, cats (the Chinese prefer cats with yellow eyes), Chinese dress, jade carving, feng shui, etiquette, the hundreds of gods of house and wayside, temples and their guardians, and all the great festivals - those of the Moon, the Dragon Boats, the Hungry Ghosts, the Magnolia, the New Year and many more. Chinese creeds and customs were Burkhardt's passion, and no better account of them will ever be written.
Translated and Edited by Sister Dorothea Olga McCants, Daughter of the Cross In Our People and Our History, originally published in French in 1911 and translated into English in 1973, Rodolphe Lucien Desdunes records the lives of fifty prominent Creoles who lived in New Orleans at the end of the nineteenth century. Although he received little formal education, Desdunes -- himself a Creole -- was an articulate observer of his times and culture. His portraits of black doctors, lawyers, teachers, musicians, artists, and writers are powerful evidence of the extraordinary role that Creoles played in the cultural and political history of Louisiana.
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