Rounding error bounds for the Clenshaw and Forsythe algorithms for the evaluation of orthogonal polynomial series

Journal of Computational and Applied Mathematics

Volumn 138, Issue 2, 2002, Pages 185-204

  Barrio, Roberto ^a  

^a UNIVERSITY OF ZARAGOZA   (Spain)

Author keywords

Orthogonal polynomials; Polynomial evaluation; Rounding error

Indexed keywords

ALGORITHMS; ERROR DETECTION; NUMERICAL METHODS;

ROUNDING ERROR BOUNDS;

POLYNOMIALS;

MODELING ERROR;

EID: 0037081333     PISSN: 03770427     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0377-0427(01)00382-X     Document Type: Article

References (18)

1. A matrix analysis of the stability of the Clenshaw algorithm
2. Perturbation simulations of rounding errors in the evaluation of Chebyshev series
3. A note on the summation of Chebyshev series
4. On Algorithms for the summation of certain special functions
5. Error analysis of an algorithm for summing certain finite series
6. Generation and use of orthogonal polynomials for data fitting with a digital computer
7. An error analysis of Goertzel's (Watt's) method for computing Fourier coefficients
8. The accuracy of solutions to triangular systems
9. A note on the evaluation of orthogonal polynomials using recurrence relations
10. Error analysis for polynomial evaluation
11. An error analysis of the modified Clenshaw method for evaluating Chebyshev and Fourier series
12. Rounding error propagation in polynomial evaluation schemes
13. Error control with polynomial evaluation
14. An algorithm for summing orthogonal polynomial series and their derivatives with applications to curve-fitting and interpolation