For computing Padé approximants, we present presumably stable recursive algorithms that follow two adjacent rows of the Padé table and generalize the well-known classical Levinson and Schur recurrences to the case of a nonnormal Padé table. Singular blocks in the table are crossed by look-ahead steps. Ill-conditioned Padé approximants are skipped also. If the size of these lookahead steps is bo...

We establish properties concerning the distribution of poles of Padé approximants, which are generic in Baire category sense. We also investigate Padé universal series, an analog of classical universal series, where Taylor partial sums are replaced with Padé approximants. In particular, we complement previous studies on this subject by exhibiting dense or closed infinite dimensional linear subs...

In this work we compare semi-discrete formulations to obtain numerical solutions for the 1D Burgers equation. The formulations consist in the discretization of the time-domain via multi-stage methods of second and fourth order: R11 and R22 Padé approximants, and of the spatial-domain via finite element methods: least-squares (MEFMQ), Galerkin (MEFG) and Streamline-Upwind Petrov-Galerkin (SUPG)....

The classical Lanczos process can be used to efficiently generate Padé approximants of the transfer function of a given single-input single-output time-invariant linear dynamical system. Unfortunately, in general, the resulting reduced-order models based on Padé approximation do not preserve the stability, and possibly passivity, of the original linear dynamical system. In this paper, we descri...

In this work, a solution strategy based on the use of Padé approximants is investigated for efficient solution of parametric finite element problems such as, for example, frequency sweep analyses. An improvement to the Padé-based expansion of the solution vector components is proposed, suggesting the advantageous a priori estimate of the poles of the solution. This allows for the intervals of a...

In this paper we generalize the notion of orthogonal Laurent polynomials to orthogonal rational functions. Orthogonality is considered with respect to a measure on the positive real line. From this, Gauss-type quadrature formulas are derived and multipoint Padé approximants for the Stieltjes transform of the measure. Convergence of both the quadrature formula and the multipoint Padé approximant...

For univariate functions the Kronecker theorem, stating the equivalence between the existence of an infinite block in the table of Padé approximants and the approximated function f being rational, is well-known. In [Lubi88] Lubinsky proved that if f is not rational, then its Padé table is normal almost everywhere: for an at most countable set of points the Taylor series expansion of f is such t...

Convergence of diagonal Padé approximants is studied for a class of functions which admit the integral representation F(λ) = r1(λ) R 1 −1 tdσ(t) t−λ + r2(λ), where σ is a finite nonnegative measure on [−1, 1], r1, r2 are real rational functions bounded at ∞, and r1 is nonnegative for real λ. Sufficient conditions for the convergence of a subsequence of diagonal Padé approximants of F on R \ [−1...