Abstract
Meshless collocation methods are often seen as a flexible alternative to overcome difficulties that may occur with other methods. As various meshless collocation methods gain popularity, finding appropriate settings becomes an important open question. Previously, we proposed a series of sequential-greedy algorithms for selecting quasi-optimal meshless trial subspaces that guarantee stable solutions from meshless methods, all of which were designed to solve a more general problem: "Let A be an M × N matrix with full rank M; choose a large M × K submatrix formed by K ≤ M columns of A such that it is numerically of full rank." In this paper, we propose a block-greedy algorithm based on a primal/dual residual criterion. Similar to all algorithms in the series, the block-greedy algorithm can be implemented in a matrix-free fashion to reduce the storage requirement. Most significantly, the proposed algorithm reduces the computational cost from the previous O(K4+NK2) to at most O(NK2). Numerical examples are given to demonstrate how this efficient and ready-to-use approach can benefit the stability and applicability of meshless collocation methods.
Original language | English |
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Pages (from-to) | A1224-A1250 |
Number of pages | 27 |
Journal | SIAM Journal on Scientific Computing |
Volume | 38 |
Issue number | 2 |
DOIs | |
Publication status | Published - 26 Apr 2016 |
Scopus Subject Areas
- Computational Mathematics
- Applied Mathematics
User-Defined Keywords
- Adaptive greedy algorithm
- Basis selection
- Kansa method
- Kernel collocation
- Radial basis function