40 research outputs found
Recursive Polynomial Remainder Sequence and the Nested Subresultants
We give two new expressions of subresultants, nested subresultant and reduced
nested subresultant, for the recursive polynomial remainder sequence (PRS)
which has been introduced by the author. The reduced nested subresultant
reduces the size of the subresultant matrix drastically compared with the
recursive subresultant proposed by the authors before, hence it is much more
useful for investigation of the recursive PRS. Finally, we discuss usage of the
reduced nested subresultant in approximate algebraic computation, which
motivates the present work.Comment: 12 pages. Presented at CASC 2005 (Kalamata, Greece, Septermber 12-16,
2005
A weakly stable algorithm for general Toeplitz systems
We show that a fast algorithm for the QR factorization of a Toeplitz or
Hankel matrix A is weakly stable in the sense that R^T.R is close to A^T.A.
Thus, when the algorithm is used to solve the semi-normal equations R^T.Rx =
A^Tb, we obtain a weakly stable method for the solution of a nonsingular
Toeplitz or Hankel linear system Ax = b. The algorithm also applies to the
solution of the full-rank Toeplitz or Hankel least squares problem.Comment: 17 pages. An old Technical Report with postscript added. For further
details, see http://wwwmaths.anu.edu.au/~brent/pub/pub143.htm
Recommended from our members
Computational complexity in multidimensional neutron transport theory calculations. Progress report, September 1, 1973--August 31, 1974
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Automated approach to quantitative error analysis. [BEAPAC-1T and -3T, for testing reliability of computer codes, in FORTRAN for IBM 370/195 and CDC 6400]
A method is described how a quantitative measure for the robustness of a given neutron transport theory code for coarse network calculations can be obtained. A code that performs this task automatically and at only nominal cost is described. This code also generates user-oriented benchmark problems which exhibit the analytic behavior at interfaces. 5 figures, 1 table