Properties of certain rational approximations toe −z

Siemieniuch, J. L.

doi:10.1007/bf01931369

Cited by 8 publications

(2 citation statements)

References 6 publications

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“…For the Restricted Pad6 approximations we know from [19], that the only A-acceptable approximations in the main diagonal are R~(z), R2(z), Ra(z) and R~(z). We also know [18],…”

Section: Stabilitymentioning

confidence: 97%

Real pole approximations to the exponential function

Orel

1991

BIT

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Abstract.Rational approximations to the exponential function with real, not necessarily distinct poles are studied in this paper. The orthogonality relation is established in order to show that the zeros of the collocation polynomial of the corresponding Runge-Kutta method are all real, simple and positive. It is proven, that approximants with the smallest error constant are the Restricted Pad6 approximants of Norsett. Some results concerning acceptability properties are given.

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“…For the Restricted Pad6 approximations we know from [19], that the only A-acceptable approximations in the main diagonal are R~(z), R2(z), Ra(z) and R~(z). We also know [18],…”

Section: Stabilitymentioning

confidence: 97%

Real pole approximations to the exponential function

Orel

1991

BIT

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“…The natural question to be discussed is therefore, what is the optimal order of such rational approximations? This problem was treated in Norsett [3] for the case where the denominator was of one of the forms (1 + y~/)~ and (1 + yq)~-i(1 + ~q) and the numerator a pol3mo-mial of degree m < n. The case of n different real zeros in the denominator and a polynomial of degree n-I in the numerator is discussed in Wolf- 1 In Siemieniuch [6] called Nsrsett approximations.…”

Section: Introductionmentioning

confidence: 99%

Attainable order of rational approximations to the exponential function with only real poles

Nørsett

Wolfbrandt

1977

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Abstract.Rational approximations of the form ~-,~=0 a~q/l'Ii=i (1 +7~q) to exp(-q), q E C, are studied with respect to order and error constant. It is shown that the maximum obtainable order is m + 1 and that the approximation of order m + 1 with bast absolute value of the error constant has ~'l =~ ..... Fn. As an application it is shown that the order of a v-stage semi-implicit Runge-Kutta method cannot exceed v + 1.

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