A New Extended Padé Approximation and Its Application

Extended discrete dipole approximation and its application to bianisotropic media.

In this research we introduce the formalism of the extension of the discrete dipole approximation to a more general range of tensorial relative permittivity and permeability. Its performance is tested in the domain of applicability of other methods for the case of composite materials (nanoshells). Then, some early results on bianisotropic nanoparticles are presented, to show the potential of th...

On Padé Approximation of Some Practical Functions

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...

A general approach to linguistic approximation and its application in frame of fuzzy logic deduction

‎This paper deals with one problem that needs to be addressed in the emerging field known under the name computing with perceptions‎. ‎It is the problem of describing‎, ‎approximately‎, ‎a given fuzzy set in natural‎ ‎language‎. ‎This problem has lately been referred to as the problem of retranslation‎. ‎An approaches to ‎dealing with the retranslation problem is discussed in the paper‎, ‎that ...

Gröbner bases and generalized Padé approximation

It is shown how to find general multivariate Padé approximation using the Gröbner basis technique. This method is more flexible than previous approaches, and several examples are given to illustrate this advantage. When the number of variables is small compared to the degree of approximation, the Gröbner basis technique is more efficient than the linear algebra methods in the literature.