高效计算模式及应用前沿ADVANCES IN THE EFFICIENCY OF COMPUTATIONAL METHODS AND APPLICATIONS

作者简介

This invaluable textbook creates a general framework for the study of optimal iterative procedures for problems that are solved approximately. Emphasis is given to the efficiency of numerical methods. For generality the setting is abstract, but the book presents many applications to practical problems, allowing the reader to take advantage of the most modern high speed calculating devices, and provides examples to illustrate concepts and major theorems. The examples are selected from astrophysics (radiative transfer and the kinetic theory of gases), mechanics (elasticity), economics (predator -- prey problems), the n-dimensional Euclidean space and other applied areas.The book will benefit not only senior undergraduates, graduates, graduate students and researchers in the field but also those who wish to obtain information about specific results or techniques that take into account the particular nature of the equation.

书籍目录

PrefaceChapter 1  Divided Differences  1.1  Partially Ordered Topological Spaces  1.2  Divided Difference in a Linear Space  1.3  Divided Differences in a Banach Space  1.4  Divided Differences and Monotone Convergence  1.5  Divided Differences and Fr@chet-derivatives  1.6  ExercisesChapter 2  Constants and Functions Appearing in Numerica Methods                                                    2.1  Preliminaries  2!  2.2  Lipschitz Conditions and Norm Estimate  3,  2.3  Lipschitz Conditions for Uryson Operators  3q  2.4  The Case X = C  3!  2.5  The Case X -- Lc~  4:  2.6  The CaseX=Lp, l

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