Abstract
A recursive method of constructing preconditioning matrices for the nonsymmetric stiffness matrix in a wavelet basis is proposed for solving a class of integral and differential equations. It is based on a level-by-level application of the wavelet scales decoupling the different wavelet levels in a matrix form just as in the well-known nonstandard form. The result is a powerful iterative method with built-in preconditioning leading to two specific algebraic multilevel iteration algorithms: one with an exact Schur preconditioning and the other with an approximate Schur preconditioning. Numerical examples are presented to illustrate the efficiency of the new algorithms.
Original language | English (US) |
---|---|
Pages (from-to) | 260-283 |
Number of pages | 24 |
Journal | SIAM Journal on Scientific Computing |
Volume | 24 |
Issue number | 1 |
DOIs | |
State | Published - 2003 |
Externally published | Yes |
Keywords
- Level-by-level transforms
- Multilevel preconditioner
- Multiresolution
- Schur complements
- Sparse approximate inverse
- Wavelets
ASJC Scopus subject areas
- Computational Mathematics
- Applied Mathematics