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Discrete wavelet transforms accelerated sparse preconditioners for dense boundary element systems. (English) Zbl 0974.65043
The author is concerned with sparse preconditioners for densely populated nonsymmetric linear algebraic systems arising from discretizations by boundary element methods. The construction is based on discrete wavelet transforms and makes use of the wavelet compression property and appropriate operator splitting techniques. The suggested wavelet transform results in transformed matrices of band structure.

MSC:
65F35 Numerical computation of matrix norms, conditioning, scaling
65N38 Boundary element methods for boundary value problems involving PDEs
65T60 Numerical methods for wavelets
35J25 Boundary value problems for second-order elliptic equations
65F10 Iterative numerical methods for linear systems
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