The Extended Euclidean algorithm for matrix Pade approximants is applied to compute matrix Pade approximants in rectangular full packed format (RFP) if the coefficient matrices of the input matrix polynomial are triangular. The procedure given by Gustavson et al for packing a triangular matrix in rectangular full packed format is applied to pack sequence of lower triangular matrices of a matrix...

Analogues of the Nuttall-Pommerenke theorem and Wallin-type theorems for classical Pade approximants, are proved for linear and nonlinear Pade approximants formed from series of orthogonal polynomials, corresponding to a distribution da(x) with at most finitely many sign changes.

We discuss the analytic continuation beyond μ T 1 in QCD at nonzero T and μ by use of the Pade’ approximants. The slope of the critical line obtained in this way increases at large μ with respect to the second order Taylor result.In the hot phase Pade’ and Taylor approximants coincide, suggesting a very large, and possibly infinite, radius of convergence of the Taylor series in this thermodynam...

It is well-known that the denominators of Pade approximants can be considered as orthogonal polynomials with respect to a linear functional. This is usually shown by defining Pade -type approximants from so-called generating polynomials and then improving the order of approximation by imposing orthogonality conditions on the generating polynomials. In the multivariate case, a similar constructi...

Ahsrruct: Section 1 describes the univariate situation in the case of non-normal Pade approximants and Cordellier’s extension of the famous five-star identity of Wynn. Section 2 repeats our definition of multivariate Pade approximants and proves a number of theorems that remain valid when going from the univariate to the multivariate case. These theorems and more new results given in Section 3....

We discuss the analytic continuation beyond μ/T ≃ 1 in QCD at nonzero T and μ by use of the Pade’ approximants. The slope of the critical line obtained in this way increases at large μ with respect to the second order Taylor result.In the hot phase Pade’ and Taylor approximants coincide, suggesting a very large, and possibly infinite, radius of convergence of the Taylor series in this thermodyn...

We present analytic estimates for the energy levels of N electrons (N = 2−5) in a two-dimensional parabolic quantum dot. A magnetic field is applied perpendicularly to the confinement plane. The relevant scaled energy is shown to be a smooth function of the parameter β=(effective Rydberg/effective dot energy)1/6. Two-point Pade approximants are obtained from the series expansions of the energy ...

We investigate the convergence of the rows (fixed denominator degree) of the Walsh array of best rational approximants to a meromorphic function. We give an explicit algorithm for determining when convergence is guaranteed and obtain rates of convergence.in the appropriate cases. This algorithm also provides the solution to an integer programming problem that arises in the study of Pade approxi...

Recently the authors have presented the d-transformation which has proved to be very efficient in accelerating the convergence of a large class of infinite series. In this work the d-transformation is modified in a way that suits power series. An economical method for computing the rational approximations arising from the modified transformation is developed. Some properties of these approximan...