The aim of this paper is to construct rational approximants for multivariate functions given by their expansion in an orthogonal polynomial system. This will be done by generalizing the concept of multivariate Padé approximation.After defining themultivariate Frobenius–Padé approximants, we will be interested in the two following problems: the first one is to develop recursive algorithms for th...

The paper reviews the relation between Padé-type approximants of a power series and interpolatory quadrature formulas with free nodes, and that between Padé approximants and Gaussian quadrature methods. Quadrature methods are well-known. They are used for obtaining an approximate value of a definite integral, and are described in any book of numerical analysis. In this talk, we will show that P...

This paper proposes a measure-theoretic reconstruction of the approximation schemes developed for Labelled Markov Processes: approximants are seen as quotients with respect to sets of temporal properties expressed in a simple logic. This gives the possibility of customizing approximants with respect to properties of interest and is thus an important step towards using automated techniques inten...

We study the convergence properties of some rational approximants for stocha-stic discrete event systems. Examples of the systems considered include computer and communication systems and general distributed and parallel processing systems. Diiculties often arise in the analysis of such systems due to the so-called \curse of dimensionality" in calculating some integer-parameterized functions, w...

The surprising recent discoveries of quasicrystals and their approximants in soft-matter systems poses the intriguing possibility that these structures can be realized in a broad range of nanoscale and microscale assemblies. It has been theorized that soft-matter quasicrystals and approximants are largely entropically stabilized, but the thermodynamic mechanism underlying their formation remain...

The temperature distribution in a conductive-radiative rectangular profiled annular fin with internal heat generation is scrutinized the present investigation. nonlinear variation of thermal conductivity and transfer coefficient governed by power law considered. analytical approximation for non-dimensional profile obtained using differential transform method (DTM)-Pade approximant. nondimension...

Abstract. The classical Gibbs phenomenon for the Fourier sections (best L2trigonometric polynomial approximants) of a jump function asserts that, near the jump, the~e sections "overshoot" the function by an asymptotically constant factor g (the L2-Gibbs constant). In this paper we show that, for a class of one-jump discontinuous functions, a similar phenomenon holds for the trigonometric polyno...

In this paper, univariate Pade approximation is applied to fractional power sries solutions of integro-differential equations with non-local boundary conditions. As it seen from comparisons, gives reliable and numerical results.

QSP-10 APPLICATION OF AN IN SILICO PHYSIOLOGICALLY BASED PHARMACOKINETIC MODEL TO SIMULATE ORAL DRUG BIOAVAILABILITY OF ATORVASTATIN ACID AND CYCLOSPORINE POST BARIATRIC SURGERY. A. S. Darwich,1 D. Pade,2 K. Rowland-Yeo,2 M. Jamei,2 A. Åsberg,3 H. Christensen,3 D. M. Ashcroft,1 A. Rostami-Hodjegan1; 1Centre for Applied Pharmacokinetic Research, University of Manchester, Manchester, United Kingd...

The univariate error formulas for Pad6 approximants and rational interpolants, which are repeated in Section 2, are generalized to the multivariate case in Section 4. We deal with "general order" multivariate Pad~ approximants and rational interpolants, where the numerator and denominator polynomials as well as the equations expressing the approximation order, can be chosen by the user of these...