Abstract. A matrix triangularization interpretation is given for the recursive algorithms computing the Padé approximants along a certain path in the Padé table, which makes it possible to unify all known algorithms in this field [5], [6]. For the normal Padé table, all these results carry over to the matrix Padé problem in a straightforward way. Additional features, resulting from the noncommu...

The low-rank damping term appears commonly in quadratic eigenvalue problems arising from physical simulations. To exploit the low-rank damping property, we propose a Padé Approximate Linearization (PAL) algorithm. The advantage of the PAL algorithm is that the dimension of the resulting linear eigenvalue problem is only n+ lm, which is generally substantially smaller than the dimension 2n of th...

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The application of the existing time-domain beampropagation method (TD-BPM) based on the finite-difference (FD) formula has been limited to the TE-mode analysis. To treat the TM mode as well as the TE mode, an improved TD-BPM is developed using a low-truncation-error FD formula with the aid of the alternating-direction implicit scheme. To improve the accuracy in time, a Padé (2,2) approximant i...

Asymptotic Padé-approximant methods are utilized to estimate the leading-order unknown (i.e., not-yetcalculated) contributions to the perturbative expansions of two-current QCD correlation functions obtained from scalar-channel fermion and gluon currents, as well as from vector-channel fermion currents. Such contributions to the imaginary part of each correlator are polynomials of logarithms wh...

Let f0 and f∞ be formal power series at the origin and infinity, and Pn/Qn, with deg(Pn), deg(Qn) 6 n, be a rational function that simultaneously interpolates f0 at the origin with order n and f∞ at infinity with order n + 1. When germs f0, f∞ represent multi-valued functions with finitely many branch points, it was shown by Buslaev [5] that there exists a unique compact set F in the complement...

The order of the post-Newtonian expansion needed to extract in a reliable and accurate manner the fully general relativistic gravitational wave signal from inspiraling compact binaries is explored. A class of approximate wave forms, called P-approximants, is constructed based on the following two inputs: ~a! the introduction of two new energy-type and flux-type functions e(v) and f (v), respect...

We consider a cellular network model with base stations configurated according to the α-Ginibre point process with α ∈ (0, 1], which is one of the determinantal point processes. In this model, we focus on the asymptotic behavior of the so-called coverage probability (or link success probability) as the threshold value tends to 0 and ∞, and discuss the Padé approximation of the coverage probabil...

Padé-approximant methods are used to estimate the three-loop perturbative contributions to the inclusive semileptonic b → u decay rate. These improved estimates of the decay rate reduce the theoretical uncertainty in the extraction of the CKM matrix element |V ub | from the measured inclusive semileptonic branching ratio. In this paper we briefly review the development of Padé approximation tec...