Sobolev Gradients and Differential Equations

Sobolev Gradients and Differential Equations

Author: John Neuberger

Publisher: Springer Science & Business Media

Published: 2009-12-01

Total Pages: 287

ISBN-13: 3642040403

DOWNLOAD EBOOK

A Sobolev gradient of a real-valued functional on a Hilbert space is a gradient of that functional taken relative to an underlying Sobolev norm. This book shows how descent methods using such gradients allow a unified treatment of a wide variety of problems in differential equations. For discrete versions of partial differential equations, corresponding Sobolev gradients are seen to be vastly more efficient than ordinary gradients. In fact, descent methods with these gradients generally scale linearly with the number of grid points, in sharp contrast with the use of ordinary gradients. Aside from the first edition of this work, this is the only known account of Sobolev gradients in book form. Most of the applications in this book have emerged since the first edition was published some twelve years ago. What remains of the first edition has been extensively revised. There are a number of plots of results from calculations and a sample MatLab code is included for a simple problem. Those working through a fair portion of the material have in the past been able to use the theory on their own applications and also gain an appreciation of the possibility of a rather comprehensive point of view on the subject of partial differential equations.


Sobolev Gradients and Differential Equations

Sobolev Gradients and Differential Equations

Author: John W. Neuberger

Publisher:

Published: 1997

Total Pages: 164

ISBN-13:

DOWNLOAD EBOOK

A Sobolev gradient of a real-valued functional is a gradient of that functional taken relative to the underlying Sobolev norm. This book shows how descent methods using such gradients allow a unified treatment of a wide variety of problems in differential equations. Equal emphasis is placed on numerical and theoretical matters. Several concrete applications are made to illustrate the method. These applications include (1) Ginzburg-Landau functionals of superconductivity, (2) problems of transonic flow in which type depends locally on nonlinearities, and (3) minimal surface problems. Sobolev gradient constructions rely on a study of orthogonal projections onto graphs of closed densely defined linear transformations from one Hilbert space to another. These developments use work of Weyl, von Neumann and Beurling.


Functional Analysis, Sobolev Spaces and Partial Differential Equations

Functional Analysis, Sobolev Spaces and Partial Differential Equations

Author: Haim Brezis

Publisher: Springer Science & Business Media

Published: 2010-11-02

Total Pages: 600

ISBN-13: 0387709142

DOWNLOAD EBOOK

This textbook is a completely revised, updated, and expanded English edition of the important Analyse fonctionnelle (1983). In addition, it contains a wealth of problems and exercises (with solutions) to guide the reader. Uniquely, this book presents in a coherent, concise and unified way the main results from functional analysis together with the main results from the theory of partial differential equations (PDEs). Although there are many books on functional analysis and many on PDEs, this is the first to cover both of these closely connected topics. Since the French book was first published, it has been translated into Spanish, Italian, Japanese, Korean, Romanian, Greek and Chinese. The English edition makes a welcome addition to this list.


Biomedical Image Registration

Biomedical Image Registration

Author: Bernd Fischer

Publisher: Springer

Published: 2010-07-05

Total Pages: 292

ISBN-13: 3642143660

DOWNLOAD EBOOK

Welcome to the proceedings of the 4th Workshop on Biomedical Image R- istration (WBIR). Previous WBIRs took place in Bled, Slovenia (1999), at the UniversityofPennsylvania,USA(2003)andinUtrecht,TheNetherlands(2006). This year, WBIR was hosted by the Institute Mathematics and Image Proce- ing and the Fraunhofer Project Group on Image Registration and it was held in Lub ̈ eck, Germany. It provided the opportunity to bring together researchers from all over the world to discuss some of the most recent advances in image registration and its applications. We had an excellent collection of papers that were reviewed by at least three reviewers each from a 35-member Program Committee assembled from a wor- wide community of registration experts. This year 17 papers were accepted for oral presentation, while another 7 papers were accepted as poster papers. We believe all of the conference papers were of excellent quality. Registration is a fundamental task in image processing used to match two or more pictures taken, for example, at di?erent times, from di?erent sensors, or from di?erent viewpoints. Establishing the correspondence of structures within medical images is fundamental to diagnosis, treatment planning, and surgical guidance. The conference papers address state-of-the-art techniques for prov- ing reliable and e?cient registration techniques, thereby imposing relationships between speci?c application areas and appropriate registration schemes. We are grateful to all those who contributed to the success of WBIR 2010.


Variational, Geometric, and Level Set Methods in Computer Vision

Variational, Geometric, and Level Set Methods in Computer Vision

Author: Nikos Paragios

Publisher: Springer

Published: 2005-10-13

Total Pages: 378

ISBN-13: 3540321098

DOWNLOAD EBOOK

Mathematical methods has been a dominant research path in computational vision leading to a number of areas like ?ltering, segmentation, motion analysis and stereo reconstruction. Within such a branch visual perception tasks can either be addressed through the introduction of application-driven geometric ?ows or through the minimization of problem-driven cost functions where their lowest potential corresponds to image understanding. The 3rd IEEE Workshop on Variational, Geometric and Level Set Methods focused on these novel mathematical techniques and their applications to c- puter vision problems. To this end, from a substantial number of submissions, 30 high-quality papers were selected after a fully blind review process covering a large spectrum of computer-aided visual understanding of the environment. The papers are organized into four thematic areas: (i) Image Filtering and Reconstruction, (ii) Segmentation and Grouping, (iii) Registration and Motion Analysis and (iiii) 3D and Reconstruction. In the ?rst area solutions to image enhancement, inpainting and compression are presented, while more advanced applications like model-free and model-based segmentation are presented in the segmentation area. Registration of curves and images as well as multi-frame segmentation and tracking are part of the motion understanding track, while - troducing computationalprocessesinmanifolds,shapefromshading,calibration and stereo reconstruction are part of the 3D track. We hope that the material presented in the proceedings exceeds your exp- tations and will in?uence your research directions in the future. We would like to acknowledge the support of the Imaging and Visualization Department of Siemens Corporate Research for sponsoring the Best Student Paper Award.


Advances in Visual Computing

Advances in Visual Computing

Author: George Bebis

Publisher: Springer

Published: 2011-09-24

Total Pages: 819

ISBN-13: 3642240283

DOWNLOAD EBOOK

The two volume set LNCS 6938 and LNCS 6939 constitutes the refereed proceedings of the 7th International Symposium on Visual Computing, ISVC 2011, held in Las Vegas, NV, USA, in September 2011. The 68 revised full papers and 46 poster papers presented together with 30 papers in the special tracks were carefully reviewed and selected from more than 240 submissions. The papers of part I (LNCS 6938) are organized in computational bioimaging, computer graphics, motion and tracking, segmentation, visualization; mapping modeling and surface reconstruction, biomedical imaging, computer graphics, interactive visualization in novel and heterogeneous display environments, object detection and recognition. Part II (LNCS 6939) comprises topics such as immersive visualization, applications, object detection and recognition, virtual reality, and best practices in teaching visual computing.


Issues in Applied Computing: 2012 Edition

Issues in Applied Computing: 2012 Edition

Author:

Publisher: ScholarlyEditions

Published: 2013-01-10

Total Pages: 95

ISBN-13: 148164825X

DOWNLOAD EBOOK

Issues in Applied Computing / 2012 Edition is a ScholarlyEditions™ eBook that delivers timely, authoritative, and comprehensive information about Materials Engineering. The editors have built Issues in Applied Computing: 2012 Edition on the vast information databases of ScholarlyNews.™ You can expect the information about Materials Engineering in this eBook to be deeper than what you can access anywhere else, as well as consistently reliable, authoritative, informed, and relevant. The content of Issues in Applied Computing: 2012 Edition has been produced by the world’s leading scientists, engineers, analysts, research institutions, and companies. All of the content is from peer-reviewed sources, and all of it is written, assembled, and edited by the editors at ScholarlyEditions™ and available exclusively from us. You now have a source you can cite with authority, confidence, and credibility. More information is available at http://www.ScholarlyEditions.com/.