The inverse scaling and squaring method for evaluating the logarithm of a matrix takes repeated square roots to bring the matrix close to the identity, computes a Padé approximant, and then scales back. We analyze several methods for evaluating the Padé approximant, including Horner’s method (used in some existing codes), suitably customized versions of the Paterson– Stockmeyer method and Van L...

We present a critical analysis of Padé-based methods for the unitarization of low energy amplitudes. We show that the use of certain Padé Approximants to describe the resonance region may lead to inaccurate determinations. In particular, we find that in the Linear Sigma Model the unitarization of the low energy amplitude through the inverse amplitude method produces essentially incorrect result...

In order to calculate the energy when 0127 is small, we expand the right-hand side of the BrillouinWigner equation in terms of a coupling constant 03BB. Both hierarchies in 0127 and 03BB are connected. The Padé approximants of the right-hand side converge. Tome 40 N° 2 15 JANVIER 1979 LE JOURNAL DE PHYSIQUE LETTRES

When s = 1 and N = ‖n‖ − 1 this is the classical Hermite Padé approximation problem. Here we allow N to be arbitrary. We describe algorithms for computing an order N genset of type n: a matrix V ∈ k[x]∗×m such that every row of V is a solution to (1) and every solution P of (1) can be expressed as a k[x]-linear combination of the rows of V . Ideally, V will be a minbasis of solutions: V has ful...

Based on the Padé approximation method, in this paper we determine the coefficients [Formula: see text] and [Formula: see text] such that [Formula: see text] where [Formula: see text] is any given integer. Based on the obtained result, we establish a more accurate formula for approximating π, which refines some known results.

The relation between the on-shell and MS mass can be expressed through scalar and vector part of the quark propagator. In principle these two-point functions have to be evaluated on-shell which is a non-trivial task at three-loop order. Instead, we evaluate the quark self energy in the limit of large and small external momentum and use conformal mapping in combination with Padé improvement in o...

In a previous paper, the author introduced a class of multivariate rational interpolants, which are called optimal Padé-type approximants (OPTA). The main goal of this paper is to extend classical results on convergence both in measure and in capacity of sequences of Padé approximants to the multivariate case using OPTA. To this end, we obtain some estimations of the size of multivariate polyno...

The method of Laplace transforms is used to find the distribution function, mean, and variance of the number of renewals of a renewal process whose inter-arrival time distribution has a rational Laplace transform. Where the Laplace transform is not rational, we use the Padé approximation method. We apply our method to certain examples and the results are compared to those reported by other rese...