Quadratically Convergent Methods

Radu Precup
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Radu Precup: Babeş-Bolyai University, Department of Applied Mathematics

Chapter Chapter 12 in Methods in Nonlinear Integral Equations, 2002, pp 195-210 from Springer

Abstract: Abstract The succesive approximation method as well as the monotone iterative methods described previously are not very fast. To explain this let us consider an operator T : X → X. All these methods give us convergent sequences (u k ) of the form $${u_{k + 1}} = T({u_k}),k \in N$$ having as limit a fixed point u * of T. For the results in Chapter 10, we have $$d({u_{k + 1}},{u^*}) \le Md({u_{k,}}{u^*})$$ .

Keywords: Banach Space; Iterative Sequence; Nonlinear Integral Equation; Order Banach Space; Quasiconvex Function (search for similar items in EconPapers)
Date: 2002
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DOI: 10.1007/978-94-015-9986-3_13

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