**Author details**

Sie Long Kek1\*, Kok Lay Teo2 and Mohd Ismail Abd Aziz3

\*Address all correspondence to: slkek@uthm.edu.my

1 Center for Research in Computational Mathematics, Universiti Tun Hussein Onn Malaysia, Parit Raja, Malaysia

2 Department of Mathematics and Statistics, Curtin University of Technology, Perth, WA, Australia

3 Department of Mathematical Sciences, Universiti Teknologi Malaysia, UTM, Skudai, Ma‐ laysia

## **References**


[15] Sethi S. P. Deterministic and stochastic optimization of a dynamic advertising model. Optimal Control Applications and Methods. 1983; 4(2):179–184. DOI: 10.1002/oca. 4660040207.

**References**

Basic Engineering. 1960; 82(1):35–45.

84 Nonlinear Systems - Design, Analysis, Estimation and Control

Athena Scientific; 1995.

Springer; 2010. p. 241–258.

Control. 2009; 5:1043–1054.

10.1080/01969722.2010.511552.

10.1016/0022‐460X(85)90291‐3.

[1] Kalman R. E. A new approach to linear filtering and prediction problems. Journal of

[2] Bryson A. E. and Ho Y. C. Applied Optimal Control. Washington: Hemisphere; 1975.

[3] Bertsekas D. P. Dynamic Programming and Optimal Control (Vol. 1, No. 2). Belmont:

[4] Lewis F. L. and Syrmos V. L. Optimal Control. 2nd ed. USA: John Wiley & Sons; 1995.

[5] Feng Z.G. and Teo K. L. Optimal feedback control for stochastic impulsive linear systems subject to Poisson processes. In: Optimization and Optimal Control. New York:

[6] Misiran M., Wu C., Lu Z. and Teo K.L. Optimal filtering of linear system driven by fractional Brownian motion. Dynamic Systems and Applications. 2010; 19(3):495–514.

[7] Loxton R., Lin Q. and Teo K. L. A stochastic fleet composition problem. Computers & Operations Research. 2012; 39(12):3177–3183. DOI: 10.1016/j.cor.2012.04.004.

[8] Liu C. M., Feng Z. G. and Teo K. L. On a class of stochastic impulsive optimal parameter selection problems. International Journal of Innovation, Computer and Information

[9] Yin Y., Shi P., Liu F. and Teo K. L. Robust L2 – L∞ filtering for a class of dynamical systems with nonhomogeneous Markov jump process. International Journal of Systems Science.

[10] Moura S. J., Fathy H. K., Callaway D. S. and Stein J. L. A stochastic optimal control approach for power management in plug‐in hybrid electric vehicles. IEEE Transactions on Control Systems Technology. 2011; 19(3):545–555. DOI: 10.1109/TCST.2010.2043736.

[11] Wiegerinck W. Broek B. V. D. and Kappen H. Stochastic optimal control in continuous space‐time multi‐agent systems. Proceedings of the 22nd Conference on Uncertainty

[12] Zhu Y. Uncertain optimal control with application to portfolio selection model. International Journal of Cybernetics and Systems. 2010; 41(7):535–547. DOI:

[13] Hać A. Suspension optimization of a 2‐DOF vehicle model using a stochastic optimal control technique. Journal of Sound and Vibration. 1985; 100(3):343–357. DOI:

[14] Todorov E. Stochastic optimal control and estimation methods adapted to the noise characteristics of the sensorimotor system. Neural Computation. 2005; 17(5):1084–1108.

in Artificial Intelligence (UAI'06), Arlington, Virginia. 2006; 528–535.

2015; 46(4):599–608. DOI: 10.1080/00207721.2013.792976.


#### **Design, Analysis, and Applications of Iterative Methods for Solving Nonlinear Systems Design, Analysis, and Applications of Iterative Methods for Solving Nonlinear Systems Design, Analysis, and Applications of Iterative Methods for Solving Nonlinear Systems**

Alicia Cordero, Juan R. Torregrosa and Maria P. Vassileva Alicia Cordero, Juan R. Torregrosa and Alicia Cordero, Juan R. Torregrosa and Maria P. Vassileva

Additional information is available at the end of the chapter Additional information is available at the end of the chapter Additional information is available at the end of the chapter

http://dx.doi.org/10.5772/64106

#### **Abstract**

In this chapter, we present an overview of some multipoint iterative methods for solving nonlinear systems obtained by using different techniques such as composition of known methods, weight function procedure, and pseudo-composition, etc. The dynamical study of these iterative schemes provides us valuable information about their stability and reliability. A numerical test on a specific problem coming from chemistry is performed to compare the described methods with classical ones and to confirm the theoretical results.

**Keywords:** system of nonlinear equations, iterative methods, order of convergence, weight function procedure, stability, basin of attraction
