Sheung Hun Cheng. Symmetric Indefinite Matrices: Linear System Solvers and Modified Inertia Problems. PhD thesis, University of Manchester, Manchester, England, January 1998. 150 pp.  Home/Search   Document Not in Database   Summary   Related Articles

....is unbounded. The theme of [4] is that pivoting strategies such as the BBK strategy that bound kLk lead to higher accuracy. A class of linear systems is given in [4] where the BBK pivoting strategy provides more accurate solutions than the BK strategy. However, a theoretical comparison by Cheng [13] of normwise and componentwise backward and forward stability of the two strategies does not identify clear superiority of the BBK strategy. Therefore with the available evidence it is not possible to conclude that the BBK strategy has superior accuracy or stability to the BK strategy for solving ....

....the multipliers in Aasen s method are bounded by 1, it is straightforward to show that if max i;j ja ij j = 1 then T has a bound illustrated for n = 5 by jT j 6 6 6 1 1 1 1 2 2 4 8 8 16 32 32 64 7 7 7 ae n 4 Whether this bound is attainable for n 4 is an open question. Cheng [13] reports experiments using direct search in which he obtained growth of 7.99 for n = 4 and 14.61 for n = 5, which are to be compared with the corresponding bounds of 16 and 64. 3.3. Aasen s Method Versus Block LDL While block LDL of a symmetric matrix using the BK pivoting strategy is ....

Sheung Hun Cheng. Symmetric Indefinite Matrices: Linear System Solvers and Modified Inertia Problems. PhD thesis, University of Manchester, Manchester, England, January 1998. 150 pp.

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