Over- and underrelaxation for linear systems with weakly cyclic jacobi matrices of index p

Wild, P.; Niethammer, Wilhelm

doi:10.1016/0024-3795(87)90058-9

Cited by 29 publications

(28 citation statements)

References 12 publications

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“…not necessarily real, with Ico-11< 1, the corresponding sets U,(R~,,p) have the same shape as described above modulo a rotation by the angle ff : = (1/p) arg (co -1 ) -arg (co) (see [18 ], the connection between hypocycloids and the SOR method was first noticed by Varga [16] ,p))] p = (I/i/) p to hold. As we shall see in Sects.…”

Section: U(ro ) : = ~\Ro(o)mentioning

confidence: 93%

“…The key for the following is an observation extensively used in [18] : One step of the SOR method (1.2) applied to a linear system with a consistently ordered p-cyclic matrix A with Jacobi matrix Jp (see (1.3) and (1.4)) is equivalent to p steps of the p-step relaxation method…”

Section: The Geometry Of a P-step Relaxation Methodsmentioning

confidence: 99%

“…contained in the open interval (1 -1/(p-2), 1) (see Wild and Niethammer [18] or Hadjidimos, Li and Varga [7]). Although the matrices J3, referred to above are three-cyclic, and the optimal co* may be obtained from (1.6) with p = 3, they may also be viewed as two-cyclic matrices.…”

Section: A(jv) ~_ [_ Fly 0]mentioning

confidence: 99%

“…2 some well-known facts of this theory. We make extensive use of the equivalence between the p-cyclic SOR method and the p-step relaxation which was considered by Galanis, Hadjidimos and Noutsos [5] and by Wild and Niethammer [18].…”

Section: A(jv) ~_ [_ Fly 0]mentioning

confidence: 99%

“…For r/> r~, U~ (R,o ' p) is empty. For a detailed geometric description of the sets U,(Ro,,p), we refer the reader to [18].…”

Section: U(ro ) : = ~\Ro(o)mentioning

confidence: 99%

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Optimal successive overrelaxation iterative methods for P-cyclic matrices

1990

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Summary.We consider linear systems whose associated block Jacobi matrices Jp are weakly cyclic of index p. In a recent paper, Pierce, Hadjidimos and Plemmons [13] proved that the block two-cyclic successive overrelaxation (SOR) iterative method is numerically more effective than the block q-cyclic SOR-method, 2 < q 2). Finally, as a counterpart to the result of Pierce, Hadjidimos and Plemmons, we show that, under this more general assumption, the two-cyclic SOR method is not always superior to the q-cyclic SOR method, 2 < q

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Section: U(ro ) : = ~\Ro(o)mentioning

confidence: 93%

Section: The Geometry Of a P-step Relaxation Methodsmentioning

confidence: 99%

Section: A(jv) ~_ [_ Fly 0]mentioning

confidence: 99%

Section: A(jv) ~_ [_ Fly 0]mentioning

confidence: 99%

“…For r/> r~, U~ (R,o ' p) is empty. For a detailed geometric description of the sets U,(Ro,,p), we refer the reader to [18].…”

Section: U(ro ) : = ~\Ro(o)mentioning

confidence: 99%