On the convergence of an iterative proceeding of Chebyshev type
Copyright policy )On the convergence of an iterative proceeding of Chebyshev type
Iterative methods are discussed for solving the operator equation \(f(x)=0\). Here \(f:X\to Y\) is a three times differentiable mapping and \(X\), \(Y\) are Banach spaces. The author considers iterative methods of the form \(x_{n+1}=x_n- D_nf(x_n)-{1\over 2} D_nf''(x_n)(D_nf(x_n))^2\), in which the unique solution \(\widehat x\) and the inverse operator \([f'(\widehat x)]^{-1}\) are approximated simultaneously by \(x_n\) and \(D_n\), respectively. Convergence and error estimates of the methods are discussed.
Banach spaces, convergence, Iterative procedures involving nonlinear operators, Newton method, error estimates, Numerical solutions to equations with nonlinear operators, nonlinear operator equation, QA1-939, iterative methods, differentiable mapping, Chebyshev method, Mathematics
Banach spaces, convergence, Iterative procedures involving nonlinear operators, Newton method, error estimates, Numerical solutions to equations with nonlinear operators, nonlinear operator equation, QA1-939, iterative methods, differentiable mapping, Chebyshev method, Mathematics
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