In this paper, we consider a new form of the arithmetic mean method for solving large block tridiagonal linear systems. The iterative method converges for systems with coefficient matrices that are symmetric positive definite or positive real or irreducible L-matrices with a strong diagonal dominance. When the coefficient matrix is symmetric positive definite, an additive preconditioner for the conjugate gradient method is derived.Both the iterative method and the preconditioner are very suitable for parallel implementation on a multivector computer. Some numerical experiments on systems resulting from the discretization of an elliptic partial differential equation are carried out on the CRAY-MP.

A parallel algorithm for solving block tridiagonal linear systems / V., Ruggiero; Galligani, Emanuele. - In: COMPUTERS & MATHEMATICS WITH APPLICATIONS. - ISSN 0898-1221. - STAMPA. - 24:(1992), pp. 15-21.

A parallel algorithm for solving block tridiagonal linear systems

GALLIGANI, Emanuele
1992

Abstract

In this paper, we consider a new form of the arithmetic mean method for solving large block tridiagonal linear systems. The iterative method converges for systems with coefficient matrices that are symmetric positive definite or positive real or irreducible L-matrices with a strong diagonal dominance. When the coefficient matrix is symmetric positive definite, an additive preconditioner for the conjugate gradient method is derived.Both the iterative method and the preconditioner are very suitable for parallel implementation on a multivector computer. Some numerical experiments on systems resulting from the discretization of an elliptic partial differential equation are carried out on the CRAY-MP.
1992
24
15
21
A parallel algorithm for solving block tridiagonal linear systems / V., Ruggiero; Galligani, Emanuele. - In: COMPUTERS & MATHEMATICS WITH APPLICATIONS. - ISSN 0898-1221. - STAMPA. - 24:(1992), pp. 15-21.
V., Ruggiero; Galligani, Emanuele
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11380/593454
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