Refinements of certain hyperbolic inequalities via the Padé approximation method

Robust Padé Approximation via SVD

Padé approximation is considered from the point of view of robust methods of numerical linear algebra, in particular the singular value decomposition. This leads to an algorithm for practical computation that bypasses most problems of solution of nearly-singular systems and spurious pole-zero pairs caused by rounding errors; a Matlab code is provided. The success of this algorithm suggests that...

On certain new refinements of Finsler-Hadwiger inequalities

Several refinements of the Finsler-Hadwiger inequality and its reverse in the triangle are discussed. A new one parameter family of Finsler-Hadwiger inequalities and their reverses are proved. This allows us to obtain new bounds for the sum of the squares of the side lengths of a triangle in terms of other elements in the triangle. Finally, these new bounds are compared to known ones.

Time Stepping Via One-Dimensional Padé Approximation

The numerical solution of time-dependent ordinary and partial differential equations presents a number of well known difficulties—including, possibly, severe restrictions on time-step sizes for stability in explicit procedures, as well as need for solution of challenging, generally nonlinear systems of equations in implicit schemes. In this note we introduce a novel class of explicit methods ba...

On Padé Approximation of Some Practical Functions

Comparison of the Padé approximation method to perturbative QCD calculations.

We present a method of estimating perturbative coefficients in Quantum Field Theory using Padé Approximants. We test this method on various known QCD results, and find that the method works very well. ? Work supported by the Department of Energy, contract DE–AC03–76SF00515. † To appear in Phys. Rev. Lett. By using the first n coefficients in a series expansion, we have estimated the (n+ 1)-st p...