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Numerical Methods for Engineers and Scientists
  • 463
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A general extrapolation algorithm
SummaryIn this paper a general formalism for linear and rational extrapolation processes is developped. This formalism includes most of the sequence transformations actually used for convergenceExpand
  • 234
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General orthogonal polynomials
In this chapter the theory of general orthogonal polynomials will be studied independently of its application to Pade approximants. This theory is not new; it can, for example, be found in a book byExpand
  • 169
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Extrapolation methods - theory and practice
Introduction to the Theory. First Steps. What is an Extrapolation Method? What is an Extrapolation Algorithm? Quasi-linear Sequence Transformations. Sequence Transformations as Ratios ofExpand
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Extrapolation methods
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History of continued fractions and Pade approximants
  • C. Brezinski
  • Mathematics, Computer Science
  • Springer series in computational mathematics
  • 20 December 1990
1 The Early Ages.- 1.1 Euclid's algorithm.- 1.2 The square root.- 1.3 Indeterminate equations.- 1.4 History of notations.- 2 The First Steps.- 2.1 Ascending continued fractions.- 2.2 The birth ofExpand
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Quasi-orthogonality with applications to some families of classical orthogonal polynomials
In this paper, we study the quasi-orthogonality of orthogonal polynomials. New results on the location of their zeros are given in two particular cases. Then these results are applied to Gegenbauer,Expand
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Generalisations de la transformation de shanks, de la table de Pade et de l'ε-algorithme
This paper deals with a generalization of the Shank's transformation for a sequence of elements of a topological vector space. It is showned how this generalization leads to a generalization of theExpand
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Lanczos-type algorithms for solving systems of linear equations
Abstract Brezinski, C. and H. Sadok, Lanczos-type algorithms for solving systems of linear equations, Applied Numerical Mathematics 11 (1993) 443–473. In this paper, a synthesis of the variousExpand
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