|
Showing 1 - 3 of
3 matches in All Departments
This is an essentially self-contained book on the theory of convex
functions and convex optimization in Banach spaces, with a special
interest in Orlicz spaces. Approximate algorithms based on the
stability principles and the solution of the corresponding
nonlinear equations are developed in this text. A synopsis of the
geometry of Banach spaces, aspects of stability and the duality of
different levels of differentiability and convexity is developed. A
particular emphasis is placed on the geometrical aspects of strong
solvability of a convex optimization problem: it turns out that
this property is equivalent to local uniform convexity of the
corresponding convex function. This treatise also provides a novel
approach to the fundamental theorems of Variational Calculus based
on the principle of pointwise minimization of the Lagrangian on the
one hand and convexification by quadratic supplements using the
classical Legendre-Ricatti equation on the other. The reader should
be familiar with the concepts of mathematical analysis and linear
algebra. Some awareness of the principles of measure theory will
turn out to be helpful. The book is suitable for students of the
second half of undergraduate studies, and it provides a rich set of
material for a master course on linear and nonlinear functional
analysis. Additionally it offers novel aspects at the advanced
level. From the contents: Approximation and Polya Algorithms in
Orlicz Spaces Convex Sets and Convex Functions Numerical Treatment
of Non-linear Equations and Optimization Problems Stability and
Two-stage Optimization Problems Orlicz Spaces, Orlicz Norm and
Duality Differentiability and Convexity in Orlicz Spaces
Variational Calculus
It was the aim of the conference to present issues in parallel
computing to a community of potential engineering/scientific users.
An overview of the state-of-the-art in several important research
areas is given by leading scientists in their field. The
classification question is taken up at various points, ranging from
parametric characterizations, communication structure, and memory
distribution to control and execution schemes. Central issues in
multiprocessing hardware and operation, such as scalability,
techniques of overcoming memory latency and synchronization
overhead, as well as fault tolerance of communication networks are
discussed. The problem of designing and debugging parallel programs
in a user-friendly environment is addressed and a number of program
transformations for enhancing vectorization and parallelization in
a variety of program situations are described. Two different
algorithmic techniques for the solution of certain classes of
partial differential equations are discussed. The properties of
domain-decomposition algorithms and their mapping onto a
CRAY-XMP-type architecture are investigated and an overview is
given of the merit of various approaches to exploiting the
acceleration potential of multigrid methods. Finally, an abstract
performance modeling technique for the behavior of applications on
parallel and vector architectures is described.
Die Behandlung kontinuierlicher und diskreter Signale und die
Beschreibung entsprechender zeitunabhangiger linearer Systeme in
Regelungs-, Nachrichten- und Digitaltechnik erfordert eine Reihe
von Transformationen, die in dem vorliegenden Text bereitgestellt
werden. Besonderer Wert wird auf die Darlegung der fur die
Anwendung wichtigen Zusammenhange zwischen verschiedenen
Transformationen gelegt. Dieses Buch ist als Begleittext einer
einschlagigen Vorlesung fur Studierende der Elektrotechnik,
Technischen Informatik oder Technomathematik gedacht.
|
|