On stable calculation of linear functionals

Gustafson, Sven-Åke

doi:10.1090/s0025-5718-1979-0521283-0

Cited by 3 publications

(1 citation statement)

References 13 publications

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“…See [7], [121 [14]. We discuss here only the case w (t)= 1, which is implemented in the subroutine CEB in [9].…”

Section: Remarkmentioning

confidence: 99%

Convergence acceleration on a general class of power series

Gustafson

1978

Computing

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Abstract-ZosammenfassungConvergence Acceleration on a General Class of Power Series. In this paper we present several efficient methods for evaluating functions defined by power series expansions. Simple computer codes for two rapid algorithms are given in a companion paper. The convergence rates of the proposed computational schemes are investigated theoretically and the results are illustrated by numerical examples.

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“…See [7], [121 [14]. We discuss here only the case w (t)= 1, which is implemented in the subroutine CEB in [9].…”

Section: Remarkmentioning

confidence: 99%

Convergence acceleration on a general class of power series

Gustafson

1978

Computing

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On the stability of a class of convergence acceleration methods for power series

Gustafson

1984

BIT

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in this paper we study the problem of evaluating the sum of a power series whose terms are given numerically with a moderate accuracy. For a large class of divergent series a sum may be defined using analytic continuation. This sum may be estimated using the values of a finite number of terms. However, it is established here that the accuracy of this estimate will generally deteriorate if we use an ever-growing number of terms. A result on the stability of product quadrature is also obtained as a corollary of our main stability theorem.

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Approximation of Analytic Functions: A Method of Enhanced Convergence

Bruno¹,

Reitich²

1994

Mathematics of Computation

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Abstract. We deal with a method of enhanced convergence for the approximation of analytic functions. This method introduces conformai transformations in the approximation problems, in order to help extract the values of a given analytic function from its Taylor expansion around a point. An instance of this method, based on the Euler transform, has long been known; recently we introduced more general versions of it in connection with certain problems in wave scattering. In §2 we present a general discussion of this approach.As is known in the case of the Euler transform, conformai transformations can enlarge the region of convergence of power series and can enhance substantially the convergence rates inside the circles of convergence. We show that conformai maps can also produce a rather dramatic improvement in the conditioning of Padé approximation. This improvement, which we discuss theoretically for Stieltjes-type functions, is most notorious in cases of very poorly conditioned Padé problems. In many instances, an application of enhanced convergence in conjunction with Padé approximation leads to results which are many orders of magnitude more accurate than those obtained by either classical Padé approximants or the summation of a truncated enhanced series.

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On stable calculation of linear functionals

Cited by 3 publications

References 13 publications

Convergence acceleration on a general class of power series

Convergence acceleration on a general class of power series

On the stability of a class of convergence acceleration methods for power series

Approximation of Analytic Functions: A Method of Enhanced Convergence

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