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The Pade approximation problem is, roughly speaking, the local approximation of analytic or meromorphic functions by rational ones. It is known to be important to solve a large scale of problems in numerical analysis, linear system theory, stochastics and other fields. There exists a vast literature on the classical Pade problem. However, these papers mostly treat the problem for functions analytic at 0 or, in a purely algebraic sense, they treat the approximation of formal power series. For certain problems however, the Pade approximation problem for formal Laurent series, rather than for...

The 1947 paper by John von Neumann and Herman Goldstine, "Numerical Inverting of Matrices of High Order" (Bulletin of the AMS, Nov. 1947), is considered as the birth certificate of numerical analysis. Since its publication, the evolution of this domain has been enormous. This book is a unique collection of contributions by researchers who have lived through this evolution, testifying about their personal experiences and sketching the evolution of their respective subdomains since the early years.

This volume generalizes the classical theory of orthogonal polynomials on the complex unit circle or on the real line to orthogonal rational functions whose poles are among a prescribed set of complex numbers. The first part treats the case where these poles are all outside the unit disk or in the lower half plane. Classical topics such as recurrence relations, numerical quadrature, interpolation properties, Favard theorems, convergence, asymptotics, and moment problems are generalized and treated in detail. The same topics are discussed for a different situation where the poles are located...

This volume generalizes the classical theory of orthogonal polynomials on the complex unit circle or on the real line to orthogonal rational functions whose poles are among a prescribed set of complex numbers. The first part treats the case where these poles are all outside the unit disk or in the lower half plane. Classical topics such as recurrence relations, numerical quadrature, interpolation properties, Favard theorems, convergence, asymptotics, and moment problems are generalized and treated in detail. The same topics are discussed for a different situation where the poles are located...

Papers presented at a workshop held at the Catholic University of Leuven, August 1981.