Springer-Verlag Berlin Heidelberg, 2011. — 440 p.This book has two faces: the first one is that of a textbook addressing itself to graduate students of mathematics and computational sciences, the second one is that of a research monograph addressing itself to numerical analysts and computational scientists working on the subject. As a textbook, selected chapters may be useful in classes on Numerical Analysis, Nonlinear Optimization, Numerical ODEs, or Numerical PDEs. The presentation is striving for structural simplicity, but not at the expense of precision. It contains a lot of theorems and proofs, from affine invariant versions of the classical Newton-Kantorovich and Newton-Mysovskikh theorem (with proofs simpler than the traditional ones) up to new convergence theorems that are the basis for advanced algorithms in large scale scientific computing. I confess that I did not work out all details of all proofs, if they were folklore or if their structure appeared repeatedly. More elaboration on this aspect would have unduly blown up the volume without adding enough value for the construction of algorithms. However, I definitely made sure that each section is self-contained to a reasonable extent. At the end of each chapter, exercises are included. Web addresses for related software are given. As a research monograph, the presentation (a) quite often goes into the depth covering a large amount of otherwise unpublished material, (b) is open in many directions of possible future research, some of which are explicitly indicated in the text. Even though the experienced reader will have no difficulties in identifying further open topics, let me mention a few of them: There is no complete coverage of all possible combinations of local and global, exact and inexact Newton or Gauss-Newton methods in connection with continuation methods—let alone of all their affine invariant realizations; in other words, the above structural matrix is far from being full. Moreover, apart from convex optimization and constrained nonlinear least squares problems, general optimization and optimal control is left out. Also not included are recent results on interior point methods as well as inverse problems in L2, even though affine invariance has just started to play a role in these fields.Contents Introduction Systems of equations: local Newton methods Systems of equations: global Newton methods Least squares problems: Gauss-Newton methods Parameter dependent systems: continuation methods Stiff ODE initial value problems ODE boundary value problems PDE boundary value problems
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Academic Press, 2008. - 272 pages.
Precise numerical analysis may be defined as the study of computer methods for solving mathematical problems either exactly or to prescribed accuracy. This book explains how precise numerical analysis is constructed.
· Clearer, simpler descriptions and explanations of the various numerical methods
· Windows based software
· Two new types...
Springer, 2008. — 387 p. 370 illus. — 3rd ed. — ISBN: 3540779736, 9783540779742
This well-accepted introduction to computational geometry is a textbook for high-level undergraduate and low-level graduate courses. The focus is on algorithms and hence the book is well suited for students in computer science and engineering. Motivation is provided from the application areas: all...
2nd edition. — Cambridge University Press, 1998. — 358 p. This is the newly revised and expanded edition of the popular introduction to the design and implementation of geometry algorithms arising in areas such as computer graphics, robotics, and engineering design. The second edition contains material on several new topics, such as randomized algorithms for polygon triangulation,...
Elsevier, 2013. — 344 pages. ISBN: 012397013X
This book is the first on the topic and explains the most cutting-edge methods needed for precise calculations and explores the development of powerful algorithms to solve research problems. Multipoint methods have an extensive range of practical applications significant in research areas such as signal processing, analysis of...
Cambridge University Press, 2007. — 1262 p.
William H. Press - Raymer Chair in Computer Sciences and Integrative Biology The University of Texas at Austin
Saul A. Teukolsky - Hans A. Bethe Professor of Physics and Astrophysics Cornell University
William T. Vetterling - Research Fellow and Director of Image Science ZINK Imaging, LLC
Brian P. Flannery - Science,...
М: ЛКИ, 2009, 480 стр.
В традиционных курсах по методам решения задач математической физики рассматриваются прямые задачи. При этом решение определяется из уравнений с частными производными, которые дополняются определенными краевыми и начальными условиями. В обратных задачах некоторые из этих составляющих постановки задачи отсутствуют. Неизвестными могут быть, например,...