The ADI Model Problem by Eugene Wachspress PDF

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4="/ : (55) If J computed with this last equation is less than 3, we may apply Eq. 52 to verify ". Equations 54–55 are adequate for most problems with real spectra that occur in practice. When k 0 > 0:1 or when higher accuracy is demanded we may use the simple relationships in Eqs. 44–50. 2 Iteration Parameters It is almost always true in applications with real spectra that the iteration parameters may be computed with an approximate formula that has negligible adverse effect on error reduction.

It happens that this choice is optimal. Although this seems evident from symmetry considerations with respect to the two eigenvalue variables, the proof is not trivial and will be given subsequently. It follows that the additional degrees of freedom in Eq. 3 of Chap. 1 lead to a more efficient scheme only when the eigenvalue intervals differ. B. Jordan’s Transformation The algorithm for J D 2n was generalized by Jordan to yield optimum parameters when the eigenvalue intervals were Œa; b and Œc; d  with a C c > 0 [Wachspress, 1963, 1966].

3) F . 4) Recalling the definition of U (after Eqs. 51) and of M (after Eqs. y/j < U Ä W . e2 ; e3 /. 0; e4 / and k 0 D u0 Ä x Ä u1 , we have from Eq. 1) By Eq. x/ Ä G: Moreover, by Eq. 4 Analysis of the Two-Variable Minimax Problem 41 From Eqs. x/ < G. u1 / D 0. u1 / D 0. x/ Moreover, by Eq. x/ < U Ä V . 4) From Eqs. x/ < G. u2 / D 0. x/j < G over Œk 0 ; 1. y/j < H . The lemma is thus proved. The construction in proof of Lemma 8 fails only when I = K = J . y/ are continuous over Œk 0 ; 1, they can alternate J times over this interval only if all their zeros are in this interval.

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