Hierarchical Approximate Proper Orthogonal Decomposition
| Autor: | Tobias Leibner, Christian Himpe, Stephan Rave |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2016 |
| Předmět: |
Applied Mathematics
Numerical analysis Parallel algorithm Numerical Analysis (math.NA) 010103 numerical & computational mathematics 01 natural sciences 010101 applied mathematics Computational Mathematics Distributed algorithm Singular value decomposition FOS: Mathematics Applied mathematics Proper orthogonal decomposition Mathematics - Numerical Analysis 0101 mathematics Computer Science::Databases Mathematics |
| Zdroj: | SIAM Journal on Scientific Computing |
| Popis: | Proper Orthogonal Decomposition (POD) is a widely used technique for the construction of low-dimensional approximation spaces from high-dimensional input data. For large-scale applications and an increasing amount of input data vectors, however, computing the POD often becomes prohibitively expensive. This work presents a generic, easy-to-implement approach to compute an approximate POD based on arbitrary tree hierarchies of worker nodes, where each worker computes a POD of only a small amount of input vectors. The tree hierarchy can be freely adapted to optimally suit the available computational resources. In particular, this hierarchical approximate POD (HAPOD) allows for both simple parallelization with low communication overhead, as well as live sequential POD computation under restricted memory capacities. Rigorous error estimates ensure the reliability of our approach, and extensive numerical examples underline its performance. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
|