ISSN:
1572-9265
Keywords:
Matrix Padé approximants
;
simultaneous Padé approximants
;
Hermite Padé approximants
;
rational approximation
Source:
Springer Online Journal Archives 1860-2000
Topics:
Computer Science
,
Mathematics
Notes:
Abstract For a vector ofk+1 matrix power series, a superfast algorithm is given for the computation of multi-dimensional Padé systems. The algorithm provides a method for obtaining matrix Padé, matrix Hermite Padé and matrix simultaneous Padé approximants. When the matrix power series is normal or perfect, the algorithm is shown to calculate multi-dimensional matrix Padé systems of type (n 0,...,n k ) inO(‖n‖ · log2‖n‖) block-matrix operations, where ‖n‖=n 0+...+n k . Whenk=1 and the power series is scalar, this is the same complexity as that of other superfast algorithms for computing Padé systems. Whenk〉1, the fastest methods presently compute these matrix Padé approximants with a complexity ofO(‖n‖2). The algorithm succeeds also in the non-normal and non-perfect case, but with a possibility of an increase in the cost complexity.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF02145386
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