| Newton Methods for Nonlinear Problems: Affine Invariance and Adaptive Algorithms 2011 Edition Contributor(s): Deuflhard, Peter (Author) |
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ISBN: 364223898X ISBN-13: 9783642238987 Publisher: Springer OUR PRICE: $80.74 Product Type: Paperback - Other Formats Published: September 2011 |
| Additional Information |
| BISAC Categories: - Mathematics | Number Systems - Computers | Computer Science - Mathematics | Differential Equations - General |
| Dewey: 510.285 |
| Series: Springer Computational Mathematics |
| Physical Information: 0.9" H x 6.1" W x 9.1" (1.35 lbs) 424 pages |
| Descriptions, Reviews, Etc. |
| Publisher Description: This book deals with the efficient numerical solution of challenging nonlinear problems in science and engineering, both in finite dimension (algebraic systems) and in infinite dimension (ordinary and partial differential equations). Its focus is on local and global Newton methods for direct problems or Gauss-Newton methods for inverse problems. The term 'affine invariance' means that the presented algorithms and their convergence analysis are invariant under one out of four subclasses of affine transformations of the problem to be solved. Compared to traditional textbooks, the distinguishing affine invariance approach leads to shorter theorems and proofs and permits the construction of fully adaptive algorithms. Lots of numerical illustrations, comparison tables, and exercises make the text useful in computational mathematics classes. At the same time, the book opens many directions for possible future research. |