Author:
Hernández-Verón M. A.,Romero N.
Abstract
AbstractIn this work, we analyze a strategy for solving symmetric algebraic Riccati equation based on the use of efficient high-order iterative scheme. This iterative scheme is more efficient than Newton’s method. Then, we propose two iterative two-stage predictor–corrector schemes using an iterative scheme with good accessibility as the predictor iteration and a high-order iterative scheme as the corrector iteration. The iterative schemes constructed turn out to be competitive compared to the commonly used Newton’s method. The efficiency of these methods is illustrated by a numerical example.
Funder
Spanish Ministry of Science.
Universidad de la Rioja
Publisher
Springer Science and Business Media LLC
Reference25 articles.
1. Amorós, C., Argyros, I.K., González, D., Magreñán, Á.A., Regmi, S., Sarría, Í.: New improvement of the domain of parameters for Newton’s method. Mathematics 8(1), 103 (2020)
2. Argyros, I.K., George, S.: Ball convergence of a sixth order iterative method with one parameter for solving equations under weak conditions. Calcolo 53, 585–595 (2016)
3. Argyros, I.K., George, S., Argyros, C.: On the complexity of convergence for high order iterative methods. J. Complex. 73, 101678 (2022)
4. Arroyo, V., Cordero, A., Torregrosa, J.R.: Approximation of artificial satellites preliminary orbits: the efficiency challenge. Math. Comput. Model. 54, 1802–1807 (2011)
5. Bartels, R.H., Stewart, G.W.: Solution of the matrix equation $$AX + XB = C$$. Algorithm 432. Commun. Ass. Comput. Mach. 15(9), 820–826 (1972)