Decker, Wolfram, Lossen, Christoph
Computing in Algebraic Geometry
A quick start using SINGULAR
Series: Algorithms and Computation in Mathematics, Vol. 16
2006, Approx. 325 p., Hardcover
ISBN: 3-540-28992-5
About this textbook
This book provides a quick access to computational tools for algebraic
geometry, the mathematical discipline which handles solution sets of polynomial
equations.
Originating from a number of intense one week schools taught by
the authors, the text is designed so as to provide a step by step
introduction which enables the reader to get started with his own
computational experiments right away. The authors present the
basic concepts and ideas in a compact way, omitting proofs and
detours, and they give references for further reading on some of
the more advanced topics. In examples and exercises, the main
emphasis is on explicit computations using the computer algebra
system SINGULAR.
The book addresses both, students and researchers. It may serve
as a basis for self-study, guiding the reader from his first
steps into computing to writing his own procedures and libraries.
Written for:
Undergraduate and graduate students in mathematics and computer
science
Keywords:
Grobner bases
computational algebraic geometry
computational commutative algebra
polynomial equations
symbolic computation
Liberti, Leo; Maculan, Nelson (Eds.)
Global Optimization
From Theory to Implementation
Series: Nonconvex Optimization and Its Applications, Vol. 84
2006, X, 428 p. 83 illus., Hardcover
ISBN: 0-387-28260-2
About this book
Most books about global optimization describe the theory of the
algorithms, whereas a given implementationfs quality never
depends exclusively on the theoretical soundness of the
algorithms that are implemented. The literature rarely discusses
the tuning of algorithmic parameters, implementation tricks,
software architectures, and the embedding of local solvers within
global solvers. And yet, there are many good software
implementations gout thereh from which the entire community
could learn something.
The scope of this book is moving a few steps toward the
systematization of the path that goes from the invention to the
implementation and testing of a global optimization algorithm.
Some of the contributors to the book are famous and some are less
well-known, but all are experts in the discipline of actually
getting global optimization to work. Thus, the papers in this
book address the following topics:
* descriptions of new implementations of general-purpose or
problem-specific global optimization algorithms;
* new algorithms in global optimization (some with numerical
results and a discussion of the implementation);
* surveys discussing existing software packages.
Table of contents
Bruaset, Are Magnus; Tveito, Aslak (Eds.)
Numerical Solution of Partial Differential Equations on
Parallel Computers
Series: Lecture Notes in Computational Science and
Engineering, Vol. 51
2006, XII, 487 p. 201 illus., 30 in colour., Softcover
ISBN: 3-540-29076-1
About this book
This book surveys the major topics that are essential to high-performance simulation on parallel computers or computational clusters. These topics, including programming models, load balancing, mesh generation, efficient numerical solvers, and scientific software, are vital ingredients in the research fields of computer science, numerical analysis, and scientific computing. In addition to presenting the technological basis, this volume addresses selected applications that combine different techniques in order to meet demanding computational challenges. Through contributions from a wide range of internationally acknowledged experts, this book gives a to-the-point and self-containing overview of efficient ways to deal with large-scale simulation problems.
Table of contents
Pavlov, Alexey, van de Wouw, Nathan, Nijmeijer, Henk
Uniform Output Regulation of Nonlinear Systems
A Convergent Dynamics Approach
Series: Systems & Control: Foundations & Applications
2006, XII, 172 p. 38 illus., Hardcover
ISBN: 0-8176-4445-8
About this textbook
The problem of asymptotic regulation of the output of a dynamical
system plays a central role in control theory. An important
variant of this problem is the output regulation problem, which
can be used in such areas as set-point control, tracking
reference signals and rejecting disturbances generated by an
external system, controlled synchronization of dynamical systems,
and observer design for autonomous systems. This book is one of
the first systematic studies on the nonlinear output regulation
problem that embraces both the local and global solvability
analysis, covering such aspects as solvability conditions,
controller design, and practical implementation issues.
The book opens with the development of the mathematical apparatus
of convergent systems?very useful for studying nonlinear control
systems?laying the foundation for most of the results presented
in the work. The study then proceeds to a new problem
statement?the so-called uniform output regulation problem. A
comprehensive solvability analysis of this problem is provided in
the next part of the work. Based on the solvability analysis,
constructive controller design methods for the global uniform
output regulation problem are presented for various classes of
nonlinear systems.
In an attempt to bridge the gap between theory and practice, the
authors conclude with a presentation of an experimental case
study. The experiment?one of the first in the field of nonlinear
output regulation?deals with control of a translational
oscillator with a rotational actuator, illustrating the
applicability of the nonlinear output regulation theory in
experiments and raising a number of questions to be addressed in
future research.
Table of contents
Preface.- Introduction.- Convergent systems.- The Uniform output
regulation problem.- Solvability of the uniform output regulation
problem.- Controller design for the global uniform output
regulation problem.- The local output regulation problem:
convergence region estimates.- Experimental case study.-
Concluding remarks.- Appendix.- References.- Index
Zivot, Eric, Wang, Jiahui
Modeling Financial Time Series with S-PLUS
2005, XXII, 1002 p. 270 illus., Softcover
ISBN: 0-387-27965-2
About this book
The field of financial econometrics has exploded over the last decade This
book represents an integration of theory, methods, and examples using the
S-PLUS statistical modeling language and the S+FinMetrics module to facilitate
the practice of financial econometrics. This is the first book to show
the power of S-PLUS for the analysis of time series data. It is written
for researchers and practitioners in the finance industry, academic researchers
in economics and finance, and advanced MBA and graduate students in economics
and finance. Readers are assumed to have a basic knowledge of S-PLUS and
a solid grounding in basic statistics and time series concepts.
This Second Edition is updated to cover S+FinMetrics 2.0 and
includes new chapters on copulas, nonlinear regime switching
models, continuous-time financial models, generalized method of
moments, semi-nonparametric conditional density models, and the
efficient method of moments.
Eric Zivot is an associate professor and Gary Waterman
Distinguished Scholar in the Economics Department, and adjunct
associate professor of finance in the Business School at the
University of Washington. He regularly teaches courses on
econometric theory, financial econometrics and time series
econometrics, and is the recipient of the Henry T. Buechel Award
for Outstanding Teaching. He is an associate editor of Studies in
Nonlinear Dynamics and Econometrics. He has published papers in
the leading econometrics journals, including Econometrica,
Econometric Theory, the Journal of Business and Economic
Statistics, Journal of Econometrics, and the Review of Economics
and Statistics.
Jiahui Wang is an employee of Ronin Capital LLC. He received a Ph.D.
in Economics from the University of Washington in 1997. He has
published in leading econometrics journals such as Econometrica
and Journal of Business and Economic Statistics, and is the
Principal Investigator of National Science Foundation SBIR grants.
In 2002 Dr. Wang was selected as one of the "2000
Outstanding Scholars of the 21st Century" by International
Biographical Centre.
The scope of questions addressed in the book, the uniformity of
their treatment, the novelty of the proposed approach, and the
obtained results make this volume unique with respect to other
works on the problem of nonlinear output regulation. In addition
to being an excellent reference for the uniform output regulation
problem, the book has a tutorial value on convergent systems. The
work will be of interest to control engineers, theorists, and
students, and may be used as a textbook for a graduate course on
nonlinear control.
Table of contents