论文信息 - High order iterative schemes for quadratic equations

High order iterative schemes for quadratic equations

High order iterative methods for quadratic equations are studied. A bi-parametric family that includes some well known iterative schemes is introduced. A unified semilocal convergence theorem is presented. The implementation and some applications to partial differential equations are finally discussed.

[1] J. Alcantud. Topological separability and axioms of countability in GPO-spaces , 1997, Bulletin of the Australian Mathematical Society.

[2] L. B. Rall,et al. Computational Solution of Nonlinear Operator Equations , 1969 .

[3] J. M. Gutiérrez,et al. A family of Chebyshev-Halley type methods in Banach spaces , 1997, Bulletin of the Australian Mathematical Society.

[4] S. Amat,et al. Third-order iterative methods under Kantorovich conditions , 2007 .

[5] José Antonio Ezquerro,et al. Chebyshev-like methods and quadratic equations , 1999 .

[6] C. DeWitt-Morette,et al. Mathematical Analysis and Numerical Methods for Science and Technology , 1990 .

[7] Sergio Amat,et al. A fast Chebyshev's method for quadratic equations , 2004, Appl. Math. Comput..

[8] Timothy A. Davis,et al. Direct methods for sparse linear systems , 2006, Fundamentals of algorithms.

[9] J. M. Gutiérrez,et al. An adaptive version of a fourth-order iterative method for quadratic equations , 2006 .

[10] S. Smale,et al. Complexity of Bézout’s theorem. I. Geometric aspects , 1993 .