Fast algorithms for dense numerical linear algebra and applications
Abstract/Contents
- Abstract
- Large-dense matrices arise in numerous applications: Boundary integral equations for elliptic partial differential equations, covariance matrices in statistics, inverse problems, radial basis function interpolation, density functional theory, multi-frontal solvers for sparse linear systems, etc. As the problem size increases, large memory requirements — scaling as O(N^2) — and extensive computational time to perform matrix algebra— scaling as O(N^2) or O(N^3) — make computations impractical. The need for fast dense numerical linear algebra is hence of utmost significance. Most of the dense matrices arising out of applications can be efficiently represented by hierarchical matrices, which are data sparse representations of certain class of dense matrices. The thesis discusses innovative algorithms for hierarchical matrices and provides a novel paradigm for constructing fast direct solvers. The thesis also presents application of these algorithms to inverse problems and filtering in the context of seismic imaging.
Description
| Type of resource | text |
|---|---|
| Form | electronic; electronic resource; remote |
| Extent | 1 online resource. |
| Publication date | 2013 |
| Issuance | monographic |
| Language | English |
Creators/Contributors
| Associated with | Ambikasaran, Sivaram |
|---|---|
| Associated with | Stanford University, Institute for Computational and Mathematical Engineering. |
| Primary advisor | Darve, Eric |
| Thesis advisor | Darve, Eric |
| Thesis advisor | Kitanidis, P. K. (Peter K.) |
| Thesis advisor | Ying, Lexing |
| Advisor | Kitanidis, P. K. (Peter K.) |
| Advisor | Ying, Lexing |
Subjects
| Genre | Theses |
|---|
Bibliographic information
| Statement of responsibility | Sivaram Ambikasaran. |
|---|---|
| Note | Submitted to the Institute for Computational and Mathematical Engineering. |
| Thesis | Thesis (Ph.D.)--Stanford University, 2013. |
| Location | electronic resource |
Access conditions
- Copyright
- © 2013 by Sivaram Ambikasaran
- License
- This work is licensed under a Creative Commons Attribution Non Commercial 3.0 Unported license (CC BY-NC).
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