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A new Fortran code, ESOLVE, is discussed for the exact solution of systems of linear equations with multiple-precision integer coefficients by congruence techniques. The code runs significantly faster than other codes which use congruential techniques. Test runs on two classes of problems reveal that the congruential method is competitive with the two-step… (More)

For k + 1 power series a 0 (z),. .. , a k (z), we present a new iterative, look-ahead algorithm for numerically computing Padé-Hermite systems and simultaneous Padé systems along a diagonal of the associated Padé tables. The algorithm computes the systems at all those points along the diagonal at which the associated striped Sylvester and mosaic Sylvester… (More)

We present new formulae for the " near " inverses of striped Sylvester and mosaic Sylvester matrices. The formulae assume computation over floating-point rather than exact arithmetic domains. The near inverses are expressed in terms of numerical Padé-Hermite systems and simultaneous Padé systems. These systems are approximants for the power series… (More)

- Stan Cabay, Anthony Jones
- 1997

In a recent paper Cabay et al. 1996a], the authors develop a fast, iterative, look-ahead algorithm for numerically computingPad e-Hermite systems and simultaneous Pad e systems along a diagonal of the associatedPad e tables. Included there is a detailed error analysis showing that the algorithm is weakly stable. In this paper, we describe a Fortran… (More)

We present a fraction-free approach to the computation of matrix Pad e systems. The method relies on determining a modiied Schur complement for the coeecient matrices of the linear systems of equations that are associated to matrix Pad e approximation problems. By using this modiied Schur complement for these matrices we are able to obtain a hybrid… (More)

DESCRIPTION Descriptions of the main algorithm, ESOLVE, and accompanying subroutines SUBBND, MRADIX, and FRADIX, together with experimental results, are given in [1]. ALGORITHM [Summary information and part of the listing is printed here. The complete listing is available from the ACM Algorithm Distribution Service (see inside back cover for order form), or… (More)

- George Labahn, Stan Cabay
- 2005

, s~p~t~ in psrt v/t~s~c #~035 ABSTRACT For matrix power series with coefficients over a field, the notion of a matrix power series remainder sequence and its corresponding cofactor sequence are introduced and developed. An algor!thm for constructing these sequences is presented. It is shown that the cofactor sequence yields directly a sequence of Padd… (More)

tire present a fraction-free approach to the computation of matrix Pad& systems. The method relies on determining a modified Schur complement for the coefficient matrices of the linear systems of equations that are associated to matrix Pad& approximation problems. By using this modified Schur complement for these matrices we are able to obtain a fast hybrid… (More)

- Stan Cabay, Bernhard Beckmnann
- 1990

For a vector of k + 1 power series we introduce two new types of rational approximations, the weak Pad&Hermite form and the weak Pad&Hermite fraction. A recurrence relation is then presented which computes Pad&Hermite forms along with their weak counterparts along a sequence of perfect points in the Pad&Hermite table. The recurrence relation results in a… (More)

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