On computational complexity in solving equations by interpolation methods,

 

Ion Păvăloiu
(Tiberiu Popoviciu Institute of Numerical Analysis)

Scanned paper: on the journal website.

Latex version of the paper.

I. Păvăloiu, On computational complexity in solving equations by interpolation methods, Rev. Anal. Numér. Théor. Approx., 24 (1995) no. 1, pp. 201-214.

[1] Brent, R., Winograd, S. and Wolfe, Ph., Optimal Iterative Processes for Root-Finding. Numer. Math. 20(5) (1973), pp. 327-341.

[2] Casulli, V. and Trigiante, D., Sui procedimenti Iterativi Compositi. Calcolo, XIII. IV (1976), pp. 403-420.

[3] Coman, Gh., Some practical Approximation Methods for Nonlinear

Equations. Mathematica Revue d’Analyse Num'{e}rique et de Th'{e}orie de l’Approximation, 11, 1-2 (1982), pp. 41-48.

[4] Kacewitcz, B., An Integral-Interpolation Iterative Method for the Soltuion of Scalar Equations, Numer. Math. 26 (4), (1976), pp. 355-365.

[5] Kung, H.T. and Traub, J.F., Optimal Order and Efficiency for Iterations With Two Evaluations. SIAM, Numer Anal. 13, 1, (1976), pp. 84-99.

[6] Ostrowski, M.A., Soltuion of Equations and Systems of Equations. Academic Press. New York and London (1960).

[7] Păvăloiu I., The Soltuion of the Equations by Interpolation (Romanian) Ed. Dacia Cluj-Napoca (1981).

[8] Păvăloiu I., Optimal Problems Concerning Interpolation Methods of Solution of Equations. Publications de L’Institut Mathematique Beograd. 52, (66), (1992), pp. 113-126.

[9] Traub, J.F., Iterative Methods for the Solution of Equations. Prentice-Hall, New York (1964).

[10] Traub, J.F., Theory of Optimal algorithms, Preprint. Department of Computer Science Carnegie-Mellon University (1973), pp. 1-22.

[11] Traub, J.F. and Wozniakowski, H., Optimal Radius of Convergence of Interpolatory Iterations for Operator Equations, Aequationes Mathematicae, 21 (1980), pp. 159-172.

[12] Turowicz, A.B., Sur les derivees d’ordre suprieur d’une fonction inverse, Ann. Polon Math.8 (1960), pp. 265-269.