This is a decommissioned version of ERA which is running to enable completion of migration processes. All new collections and items and all edits to existing items should go to our new ERA instance at https://ualberta.scholaris.ca - Please contact us at erahelp@ualberta.ca for assistance!
- 198 views
- 197 downloads
A Stable Algorithm for Multi-dimensional Padé Systems and the Inversion of Generalized Sylvester Matrices
-
- Author(s) / Creator(s)
-
Technical report TR94-07. For k+1 power series a0(z), ..., ak(z), we present a new iterative, look-ahead algorithm for numerically computing Pade'-Hermite systems and simultaneous Pade' systems along a diagonal of the associated Pade' tables. The algorithm computes the systems at all those points along the diagonal at which the associated striped Sylvester and mosaic Sylvester matrices are well-conditioned. It is shown that a good estimate for the condition numbers of these Sylvester matrices at a point is easily determined from the Pade'-Hermite system and simultaneous Pad'e system computed at that point. The operation and the stability of the algorithm is controlled by a single parameter tau which serves as a threshold in deciding if the Sylvester matrices at a point are sufficiently well-conditioned. We show that the algorithm is weakly stable, and provide bounds for the error in the computed solutions as a function of tau. Experimental results are given which show that the bounds reflect the actual behavior of the error. The algorithm requires O(||n||^2 + s^2 ||n||) operations, to compute Pade'-Hermite and simultaneous Pade' systems of type n=[n0, ..., nk], where ||n|| = n0 + ... + nk and s is the largest step-size taken along the diagonal. An additional application of the algorithm is the stable inversion of striped and mosaic Sylvester matrices. | TRID-ID TR94-07
-
- Date created
- 1994
-
- Type of Item
- Report
-
- License
- Attribution 3.0 International