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Full-Text Articles in Physical Sciences and Mathematics
Stability Of A Pivoting Strategy For Parallel Gaussian Elimination, Jodi Mead, R. Renaud, B. Welfert
Stability Of A Pivoting Strategy For Parallel Gaussian Elimination, Jodi Mead, R. Renaud, B. Welfert
Jodi Mead
Gaussian elimination with partial pivoting achieved by adding the pivot row to the kth row at step k, was introduced by Onaga and Takechi in 1986 as means for reducing communications in parallel implementations. In this paper it is shown that the growth factor of this partial pivoting algorithm is bounded above by n <#60; 3 n–1, as compared to 2 n–1 for the standard partial pivoting. This bound n, close to 3 n–2, is attainable for class of near-singular matrices. Moreover, for the same matrices the growth factor is small under partial pivoting.
The Y-Triangle Move Does Not Preserve Intrinsic Knottedness, Ramin Naimi, Erica Flapan
The Y-Triangle Move Does Not Preserve Intrinsic Knottedness, Ramin Naimi, Erica Flapan
Ramin Naimi
We answer the question "Does the Y-triangle move preserve intrinsic knottedness?" in the negative by giving an example of a graph that is obtained from the intrinsically knotted graph K_7 by triangle-Y and Y-triangle moves but is not intrinsically knotted.