Sobolev gradients and differential equations (Record no. 3161)
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000 -LEADER | |
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fixed length control field | 02753nam a22002177a 4500 |
003 - CONTROL NUMBER IDENTIFIER | |
control field | OSt |
005 - DATE AND TIME OF LATEST TRANSACTION | |
control field | 20240829160309.0 |
008 - FIXED-LENGTH DATA ELEMENTS--GENERAL INFORMATION | |
fixed length control field | 220621b |||||||| |||| 00| 0 eng d |
020 ## - INTERNATIONAL STANDARD BOOK NUMBER | |
International Standard Book Number | 9783642040405 |
040 ## - CATALOGING SOURCE | |
Transcribing agency | Donation by Prof. A S Vasudeva Murthy |
Original cataloging agency | ICTS-TIFR |
050 ## - LIBRARY OF CONGRESS CALL NUMBER | |
Classification number | QA3 |
100 ## - MAIN ENTRY--PERSONAL NAME | |
Personal name | Neuberger, J. W. |
245 ## - TITLE STATEMENT | |
Title | Sobolev gradients and differential equations |
Remainder of title | - 2nd Ed. |
250 ## - EDITION STATEMENT | |
Edition statement | 2nd ed. |
260 ## - PUBLICATION, DISTRIBUTION, ETC. | |
Place of publication, distribution, etc. | New York: |
Name of publisher, distributor, etc. | Springer, |
Date of publication, distribution, etc. | [c1997] |
300 ## - Physical Description | |
Pages: | 289 p |
490 ## - SERIES STATEMENT | |
Series statement | Lecture Notes in Mathematics |
Volume/sequential designation | 1670 |
505 ## - FORMATTED CONTENTS NOTE | |
Formatted contents note | 1. Several Gradients<br/>2. Comparison of Two Gradients<br/>3. Continuous Steepest Descent in Hilbert Space: Linear Case<br/>4. Continuous Steepest Descent in Hilbert Space: Nonlinear Case<br/>5. Orthogonal Projections, Adjoints and Laplacians<br/>6. Ordinary Differential Equations and Sobolev Gradients<br/>7. Convexity and Gradient Inequalities<br/>8. Boundary and Supplementary Conditions<br/>9. Continuous Newton’s Method<br/>10. More About Finite Differences<br/>11. Sobolev Gradients for Variational Problems<br/>12. An Introduction to Sobolev Gradients in Non-Inner Product Spaces<br/>13. Singularities and a Simple Ginzburg-Landau Functional<br/>14. The Superconductivity Equations of Ginzburg-Landau<br/>15. Tricomi Equation: A Case Study<br/>16. Minimal Surfaces<br/>17. Flow Problems and Non-Inner Product Sobolev Spaces<br/>18. An Alternate Approach to Time-dependent PDEs<br/>19. Foliations and Supplementary Conditions I<br/>20. Foliations and Supplementary Conditions II<br/>21. Some Related Iterative Methods for Differential Equations<br/>22. An Analytic Iteration Method<br/>23. Steepest Descent for Conservation Equations<br/>24. Code for an Ordinary Differential Equation<br/>25. Geometric Curve Modeling with Sobolev Gradients<br/>26. Numerical Differentiation, Sobolev Gradients<br/>27. Steepest Descent and Newton’s Method and Elliptic PDE<br/>28. Ginzburg-Landau Separation Problems<br/>29. Numerical Preconditioning Methods for Elliptic PDEs<br/>30. More Results on Sobolev Gradient Problems<br/>31. Notes and Suggestions for Future Work |
520 ## - SUMMARY, ETC. | |
Summary, etc. | 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. |
942 ## - ADDED ENTRY ELEMENTS (KOHA) | |
Source of classification or shelving scheme | |
Koha item type | Book |
Withdrawn status | Lost status | Damaged status | Not for loan | Collection code | Home library | Shelving location | Date acquired | Inventory number | Full call number | Accession No. | Koha item type |
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Mathematics | ICTS | Rack No 3 | 06/21/2022 | Gratis | QA3 | 02533 | Book |