An Alternating-Direction-Implicit Iteration Technique

Wachspress, Eugene L.; Habetler, G. J.

doi:10.1137/0108027

Cited by 95 publications

(34 citation statements)

References 10 publications

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“…This idea, in the context of ADI methods, goes back to Wachspress and Habetler [59]; see also [58, p. 242]. It is straightforward to see that this is equivalent to applying the alternating iteration (2.1) to the symmetrically preconditioned system…”

Section: The Alternating Splitting Iterationmentioning

confidence: 99%

A Preconditioner for Generalized Saddle Point Problems

Benzi¹,

Golub²

2004

SIAM J. Matrix Anal. & Appl.

386

271

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Abstract. In this paper we consider the solution of linear systems of saddle point type by preconditioned Krylov subspace methods. A preconditioning strategy based on the symmetric/ skew-symmetric splitting of the coefficient matrix is proposed, and some useful properties of the preconditioned matrix are established. The potential of this approach is illustrated by numerical experiments with matrices from various application areas.

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Section: The Alternating Splitting Iterationmentioning

confidence: 99%

A Preconditioner for Generalized Saddle Point Problems

Benzi¹,

Golub²

2004

SIAM J. Matrix Anal. & Appl.

386

271

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“…That is to say, we may choose a set of parameters { j ; j } m j=1 such that the quantity ( Now, similar to the result in Reference [16], we can obtain the following theorem which can reduce the m-parameter problem (13) to a m=2-parameter problem when the m is even. Therefore, if m = 2 p with p a given positive integer, by repeating this process we can eventually obtain a one-parameter problem which can be solved directly.…”

Section: The Commutative Casementioning

confidence: 77%

Two‐step waveform relaxation methods for implicit linear initial value problems

Pan

Bai

2004

Numerical Linear Algebra App

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SUMMARYA class of two-step waveform relaxation methods is established and studied for solving implicit linear initial value problems, which, in particular, includes the alternating direction implicit waveform relaxation (ADIWR) methods. The convergence property of the ADIWR methods is studied in depth under suitable conditions, and their computing behaviour is illustrated by numerical examples. Moreover, we discuss about the choice of the optimal parameters involved in the ADIWR methods.

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“…By the analysis in Section 2, A 1 and A 2 are symmetric, positive definite, and commutative. Therefore, the ADI method (5) with Wachspress parameters [12,13] has a convergence rate of OϪlog h Ϫ1 for h max{h x ; h y }: Thus, denoting the convergence rate on a grid with mesh size h by r(h), we can assume that…”

Section: Single Grid High-order Adimentioning

confidence: 99%