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- W2561179999 abstract "SUMMARY Applying a finite difference approximation to a biharmonic equation results in a very ill-conditioned system of equations. This paper examines the conjugate gradient method ' used in con junction with the generalized and approximate polynomial preconditionings for solving such linear systems. An approximate polynomial preconditioning is introduced, and is shown to be more efficient than the generalized polynomial preconditionings. This new technique provides a simple but effective preconditioning polynomial, which is based on another coefficient matrix rather than the original matrix operator as commonly used. INTRODUCTION The conjugate gradient (CG) method used in conjunction with a suitable preconditioning has been widely accepted as one of the most efficient iterative procedures for solving large and sparse systems of linear equations. The basic CG algorithm can be efficiently implemented on a vector computer. However, the traditional preconditioning technique, which is generally based on an incomplete LU factorization procedure (Meijerink and van der Vorst," @default.
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- W2561179999 date "1987-01-01" @default.
- W2561179999 modified "2023-09-26" @default.
- W2561179999 title "Approximate Polynomial Preconditioning Applied to Biharmonic Equations on Vector Supercomputers" @default.
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