ERA users may experience an intermittent Deposit/Save error. We apologize for any inconvenience this may cause. Thank you for your patience while we work to resolve the issue. When the work is completed, we'll remove this notice.
- 51 views
- 68 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 a_0(z), ..., a_k(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=[n_0, ..., n_k], where ||n|| = n_0 + ... + n_k 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