| Hierarchical Matrices: A Means to Efficiently Solve Elliptic Boundary Value Problems 2008 Edition Contributor(s): Bebendorf, Mario (Author) |
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ISBN: 3540771468 ISBN-13: 9783540771463 Publisher: Springer OUR PRICE: $170.99 Product Type: Paperback - Other Formats Published: June 2008 Annotation: Hierarchical matrices are an efficient framework for large-scale fully populated matrices arising, e.g., from the finite element discretization of solution operators of elliptic boundary value problems. In addition to storing such matrices, approximations of the usual matrix operations can be computed with logarithmic-linear complexity, which can be exploited to setup approximate preconditioners in an efficient and convenient way. Besides the algorithmic aspects of hierarchical matrices, the main aim of this book is to present their theoretical background. The book contains the existing approximation theory for elliptic problems including partial differential operators with nonsmooth coefficients. Furthermore, it presents in full detail the adaptive cross approximation method for the efficient treatment of integral operators with non-local kernel functions.The theory is supported by many numerical experiments from real applications. |
| Additional Information |
| BISAC Categories: - Mathematics | Matrices - Mathematics | Number Systems - Mathematics | Differential Equations - Partial |
| Dewey: 515.353 |
| Series: Lecture Notes in Computational Science and Engineering |
| Physical Information: 0.8" H x 6.1" W x 9.2" (1.20 lbs) 296 pages |
| Descriptions, Reviews, Etc. |
| Publisher Description: Hierarchical matrices are an efficient framework for large-scale fully populated matrices arising, e.g., from the finite element discretization of solution operators of elliptic boundary value problems. In addition to storing such matrices, approximations of the usual matrix operations can be computed with logarithmic-linear complexity, which can be exploited to setup approximate preconditioners in an efficient and convenient way. Besides the algorithmic aspects of hierarchical matrices, the main aim of this book is to present their theoretical background. The book contains the existing approximation theory for elliptic problems including partial differential operators with nonsmooth coefficients. Furthermore, it presents in full detail the adaptive cross approximation method for the efficient treatment of integral operators with non-local kernel functions. The theory is supported by many numerical experiments from real applications. |