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

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

Automated approach to quantitative error analysis. [BEAPAC-1T and -3T for testing reliability of computer codes, in FORTRAN for IBM 370/195]

A method is developed concerning 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 nomial cost is described. This code also generates user-oriented benchmark problems which exhibit the analytic behavior at interfaces. 2 figures. (RWR