Problem 1 (Convergence of Richardson iteration). This method’s operator has the form T = I − BA = I − ωA because B = ωI. The eigenvectors of T are – as is easy to verify, the same as those of A, and the eigenvalues of T are λi(T ) = 1− ωλi(A). To prove that the method converges, it is convenient to verify that the l2 norm of T is less than one because we can then express everything in terms of ...

The numerical analysis of various modeling formalisms (4, 10, 141 profits from a structured representation for the generator matrix Q of the underlying continuous time Markov chain, where Q is described by a sum of tensor (kronecker) products of much smaller matrices. In this paper we describe such a representation for the class of superposed generalized stochastic Petri nets (SGSPNS), which is...

The current state of software development for numerical simulation is unnecessarily cumbersome and time consuming. The language numerical analysts use to communicate ideas with each other is fairly standard, even across language barriers. There have been successful e orts in computer aided designing (CAD) and visualization to make software systems which are designed so that tasks are performed ...

System theory for numerical analysis has recently become a focus of research. In this paper we regard dynamics of Newton’s method as a nonlinear feedback system and derive convergence conditions, based on the internal model principle and systems of Lur’e type. We then focus our attention on the analysis of the region of absolute stability of Runge-Kutta type methods. We derive a linear matrix i...

We present a new numerical abstract domain for static analysis of the errors introduced by the approximation by floating-point arithmetic of real numbers computation, by abstract interpretation [3]. This work extends a former domain [4,8], with an implicitly relational domain for the approximation of the floating-point values of variables, based on affine arithmetic [2]. It allows us to analyze...

In signal processing, discrete convolutions are usually involved in fast calculating coefficients of time-frequency decompositions like wavelet and Gabor frames. Depending on the regularity of the mother analyzing functions, one wants to detect the right resolution in order to achieve good approximations of coefficients. Local–global conditions on functions in order to get the convergence rate ...

This paper is devoted to the study of asymptotic zero distribution of Laurent-type approximants under certain extremality conditions analogous to the condition of Grothmann 1], which can be traced back t o W alsh's theory of exact harmonic majorants 8, 9]. We a l s o p r o ve results on the convergence of ray sequences of Laurent-type approximants to a function analytic on the closure of a nite...