AbstractRounding error bounds of the Forsythe and the Clenshaw–Smith algorithm for the evaluation of finite series of orthogonal polynomials are presented. The forward error is studied by means of a direct approach that permits to obtain sharp bounds. The bounds are illustrated with several numerical tests
International audienceLet $u$ denote the relative rounding error of some floating-point format. Rece...
AbstractThe problem of the evaluation in floating-point arithmetic of a polynomial with floating-poi...
A roundoff error analysis of the Lagrange interpolation formula for evaluating polynomials is perfor...
AbstractRounding error bounds of the Forsythe and the Clenshaw–Smith algorithm for the evaluation of...
AbstractIn this paper, we present rounding error bounds of recent parallel versions of Forsythe's an...
AbstractThe error propagation characteristics of the polynomial evaluation schemes of Horner, Clensh...
A roundoff error analysis of formulae for evaluating polynomials is performed. The considered formul...
This paper presents some numerical simulations of rounding errors produced during evaluation of Cheb...
Some remarks on the numerical evaluation of recurrence relations are presented. Results concerning t...
The Horner and Goertzel algorithms are frequently used in polynomial evaluation. Each of them can be...
This paper presents a generic condition number for polynomials that is useful for polynomial evaluat...
Floating point error is an inevitable drawback of embedded systems implementation. Computing rigorou...
18 pages, 2 tables, 1 figureInternational audienceA longstanding problem related to floating-point i...
A longstanding problem related to floating-point implementation of numerical programs is to provide ...
Roundoff errors cannot be avoided when implementing numerical programs with finite precision. The ab...
International audienceLet $u$ denote the relative rounding error of some floating-point format. Rece...
AbstractThe problem of the evaluation in floating-point arithmetic of a polynomial with floating-poi...
A roundoff error analysis of the Lagrange interpolation formula for evaluating polynomials is perfor...
AbstractRounding error bounds of the Forsythe and the Clenshaw–Smith algorithm for the evaluation of...
AbstractIn this paper, we present rounding error bounds of recent parallel versions of Forsythe's an...
AbstractThe error propagation characteristics of the polynomial evaluation schemes of Horner, Clensh...
A roundoff error analysis of formulae for evaluating polynomials is performed. The considered formul...
This paper presents some numerical simulations of rounding errors produced during evaluation of Cheb...
Some remarks on the numerical evaluation of recurrence relations are presented. Results concerning t...
The Horner and Goertzel algorithms are frequently used in polynomial evaluation. Each of them can be...
This paper presents a generic condition number for polynomials that is useful for polynomial evaluat...
Floating point error is an inevitable drawback of embedded systems implementation. Computing rigorou...
18 pages, 2 tables, 1 figureInternational audienceA longstanding problem related to floating-point i...
A longstanding problem related to floating-point implementation of numerical programs is to provide ...
Roundoff errors cannot be avoided when implementing numerical programs with finite precision. The ab...
International audienceLet $u$ denote the relative rounding error of some floating-point format. Rece...
AbstractThe problem of the evaluation in floating-point arithmetic of a polynomial with floating-poi...
A roundoff error analysis of the Lagrange interpolation formula for evaluating polynomials is perfor...
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