1. Numerical behaviour of multigrid methods for symmetric Sinc–Galerkin systems.
- Author
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Ng, Michael K., Serra-Capizzano, Stefano, and Tablino-Possio, Cristina
- Subjects
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SYMMETRIC matrices , *MATRICES (Mathematics) , *MULTIGRID methods (Numerical analysis) , *NUMERICAL analysis , *MATHEMATICAL analysis , *ALGEBRA - Abstract
The symmetric Sinc–Galerkin method developed by Lund (Math. Comput. 1986; 47:571–588), when applied to second-order self-adjoint boundary value problems on d dimensional rectangular domains, gives rise to an N × N positive definite coefficient matrix which can be viewed as the sum of d Kronecker products among d - 1 real diagonal matrices and one symmetric Toeplitz-plus-diagonal matrix. Thus, the resulting coefficient matrix has a strong structure so that it can be advantageously used in solving the discrete system. The main contribution of this paper is to present and analyse a multigrid method for these Sinc–Galerkin systems. In particular, we show by numerical examples that the solution of a discrete symmetric Sinc–Galerkin system can be obtained in an optimal way only using O(N log N) arithmetic operations. Numerical examples concerning one- and two-dimensional problems show that the multigrid method is practical and efficient for solving the above symmetric Sinc–Galerkin linear system. Copyright © 2004 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]
- Published
- 2005
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