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On two variants of an algebraic wavelet preconditioner. (English) Zbl 1013.65040

Summary: 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.

MSC:

65F35 Numerical computation of matrix norms, conditioning, scaling
65Y20 Complexity and performance of numerical algorithms
65F10 Iterative numerical methods for linear systems
65N06 Finite difference methods for boundary value problems involving PDEs
65T60 Numerical methods for wavelets
35J25 Boundary value problems for second-order elliptic equations
65N55 Multigrid methods; domain decomposition for boundary value problems involving PDEs

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