The scaling and squaring method is the most widely used method for computing the matrix exponential, not least because it is the method implemented in MATLAB’s expm function. The method scales the matrix by a power of 2 to reduce the norm to order 1, computes a Padé approximant to the matrix exponential, and then repeatedly squares to undo the effect of the scaling. We give a new backward error...

We present a prediction for the four loop β-function for SQCD based on the method

The Padé approximation is a useful method for creating new inequalities and improving certain inequalities. In this paper we use the Padé approximant to give the refinements of some remarkable inequalities involving inverse trigonometric functions, it is shown that the new inequalities presented in this paper are more refined than that obtained in earlier papers.

Previously developed Padé–related method of resummation for QCD observables, which achieves exact renormalization–scale–invariance, is extended so that the scheme–invariance is obtained as well. The dependence on the leading scheme parameter c2 is eliminated by a variant of the method of the principle of minimal sensitivity. The subleading parameter c3 in the approximant is then fixed in such a...

A new complex Jacobi iterative technique adapted for the solution of three-dimensional (3D) non-paraxial beam propagation is presented. The beam propagation equation for analysis of optical propagation in waveguide structures is based on a novel modified Padé(1,1) approximant operator we recently proposed. The effectiveness of our new approach is demonstrated in comparison with the traditional ...

Padé approximant is exploited for an efficient sum-over-poles decomposition of Fermi and Bose functions. The resulting poles are all pure imaginary and can therefore be used to define Padé frequencies, in analogy with the celebrated Matsubara frequencies. The proposed Padé spectrum decomposition is shown to be equivalent to a truncated continued fraction. It converges significantly faster than ...

The purpose of this study is to approximate the stream function and temperature distribution of the MHD flow in a laminar liquid film from a horizontal stretching surface. In this paper DTM-Padé method was used which is a combination of differential transform method DTM and Padé approximant. The DTM solutions are only valid for small values of independent variables. Comparison between the solut...

Within the context of massive N -component φ scalar field theory, we use asymptotic Padéapproximant methods to estimate from prior orders of perturbation theory the five-loop contributions to the coupling-constant β-function βg, the anomalous mass dimension γm, the vacuum-energy βfunction βv, and the anomalous dimension γ2 of the scalar field propagator. These estimates are then compared with e...