Titlebook: Laurent Series and their Padé Approximations; Adhemar Bultheel Book 1987 Springer Basel AG 1987 Finite.Matrix.Meromorphic function.algorit

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0255-0156 t Pade approximation problem can be solved. In that case, two series are approximated, one is a power series in z and the other is a power series in z-l. So we can approximate two, not necessarily different functions one at zero and the other at infinity.978-3-0348-9988-8978-3-0348-9306-0Series ISSN 0255-0156 Series E-ISSN 2296-4878

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Determination of poles, complicated situation occurs where Rutishauser polynomials are needed. Again, when . goes to ± ∞, these Rutishauser polynomials will converge to some polynomials whose zeros give a number of the poles of the given meromorphic function. This generalizes the results of theorem 13.1. Similar results for zeros will be derived in the next chapter.

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Two algorithms,n the Padé table. The algorithms are well known methods for the solution of Toeplitz systems [TRE1], [ZOH1] and are related to the methods of Levinson and Schur known in digital filtering theory. Much information on these algorithms and many related ones can be found in a thesis by D.R.Sweet [SWE].

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Determinant expressions and matrix interpretations,thms 1 and 2. In subsequent chapters we gave interpretations in terms of Padé approximants, continued fractions, Moebius transforms and orthogonal polynomials. In this chapter we shall come back to the linear algebra and show how the previous results may be interpreted in this environment.