Crystal Structure Analysis using Superposition, by E. Hohne

By E. Hohne

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Great care needs to be taken when introducing preconditioning matrices into parallel computation. References 1. ) Parallel Mathematics, 1977. 2. Lord, R E, Kowalik, J S and Kumar, S P, Solving Linear Algebraic Equations on an MIMD Computer, J. of ACM, Jan 1983. 3. Kuck, D J, A survey of parallel machine organization and programming, Computing Surveys 9, 29-59, 1977. 4. M. 25, 31-91, 1978. 5. Sorenson, D, Lecture presented at XIV Mathematical Programming Symposium, Boston, 1985. 6. ) Parallel Computing 1985, Elsevier Science.

That is, whenever two nonzero quantities are added or subtracted, the result is nonzero. This means that in the analysis we ignore any zeros which might be created through exact cancellation. Such cancellation rarely occurs, and any such prediction would be difficult in general, particularly in floating point arithmetic which is subject to rounding errors. Now let us return to the issue of whether A has a triangular factorization, and even if it does, whether it can be computed in a numerically stable manner.

Lord, R E, Kowalik, J S and Kumar, S P, Solving Linear Algebraic Equations on an MIMD Computer, J. of ACM, Jan 1983. 3. Kuck, D J, A survey of parallel machine organization and programming, Computing Surveys 9, 29-59, 1977. 4. M. 25, 31-91, 1978. 5. Sorenson, D, Lecture presented at XIV Mathematical Programming Symposium, Boston, 1985. 6. ) Parallel Computing 1985, Elsevier Science. 7. Modi, J J and Clarke, M R B, An alternative Givens ordering, Numer. Math. 43, 83-90, 1984. 8. Kowalik, J S, Kumar S P and Kangria, E R, An implementation of the fast Givens transformation on an MIMD computer, Applications Mathematicae, Polish Academy of Sciences, 1983.

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