期刊
JOURNAL OF SCIENTIFIC COMPUTING
卷 57, 期 3, 页码 477-501出版社
SPRINGER/PLENUM PUBLISHERS
DOI: 10.1007/s10915-013-9714-z
关键词
Fast direct solver; Numerical linear algebra; Partial hierarchically semi-separable representation; Hierarchical matrix; Radial basis function
资金
- Army High Performance Computing Research Center (AHPCRC)
- The Global Climate and Energy Project (GCEP) at Stanford
- Division Of Mathematical Sciences
- Direct For Mathematical & Physical Scien [1228275] Funding Source: National Science Foundation
This article describes a fast direct solver (i.e., not iterative) for partial hierarchically semi-separable systems. This solver requires a storage of and has a computational complexity of arithmetic operations. The numerical benchmarks presented illustrate the method in the context of interpolation using radial basis functions. The key ingredients behind this fast solver are recursion, efficient low rank factorization using Chebyshev interpolation, and the Sherman-Morrison-Woodbury formula. The algorithm and the analysis are worked out in detail. The performance of the algorithm is illustrated for a variety of radial basis functions and target accuracies.
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