Global Identities in the Non-normal Newton-Padé Approximation Table

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...

Generalized Cayley-Hamilton-Newton identities

The q-generalizations of the two fundamental statements of matrix algebra – the Cayley-Hamilton theorem and the Newton relations – to the cases of quantum matrix algebras of an ”RTT-” and of a ”Reflection equation” types have been obtained in [2]–[6]. We construct a family of matrix identities which we call Cayley-HamiltonNewton identities and which underlie the characteristic identity as well ...

Newton Identities for Weierstrass Products

We prove a generalization of the Newton Identities for entire functions, which give a relation between the Taylor coefficients and sums of powers of reciprocals of the zeros of an entire function. We apply these identities to a number of special functions, yielding some interesting recursion relations. By the Weierstrass Product Theorem, any entire function f : C → C can be written as a normall...

On the Froissart phenomenon in multivariate homogeneous Padé approximation

In univariate Padé approximation we learn from the Froissart phenomenon that Padé approximants to perturbed Taylor series expansions of rational functions exhibit almost cancelling polezero combinations that are unwanted. The location of these pole-zero pairs is given by the socalled Froissart polynomial. In this paper the occurrence of the Froissart phenomenon is explored for the first time in...