0 IntroductionWe seek methods for obtaining a simple zero x~* of the function f(x).The aim isto develop iterative processes of order p,in the error equationε_(k+1)=Kε_k^p+O(ε_k^(p+1)),as ε_k→0for ε_k=x_k-x~* and...0 IntroductionWe seek methods for obtaining a simple zero x~* of the function f(x).The aim isto develop iterative processes of order p,in the error equationε_(k+1)=Kε_k^p+O(ε_k^(p+1)),as ε_k→0for ε_k=x_k-x~* and Ka function only of the derivatives of f at x~*.The methods to be discussed require one function evaluation and several 1-orderderivative evaluations.They have the advantage when the derivative f^(?) can be ob-展开更多
Let f*g (z) be the convolution or Hadamard product of two functiom f(z) and g(z), that is, if f (z) =z+sum from n=2 to ∞a_nz^n and g(z) =z+sum from n=2 to ∞b_n z_n, then f*g(z)=z+sum from n=2 to ∞a_n b_n z^n (1) Le...Let f*g (z) be the convolution or Hadamard product of two functiom f(z) and g(z), that is, if f (z) =z+sum from n=2 to ∞a_nz^n and g(z) =z+sum from n=2 to ∞b_n z_n, then f*g(z)=z+sum from n=2 to ∞a_n b_n z^n (1) Let T denote the class of functions of the展开更多
文摘0 IntroductionWe seek methods for obtaining a simple zero x~* of the function f(x).The aim isto develop iterative processes of order p,in the error equationε_(k+1)=Kε_k^p+O(ε_k^(p+1)),as ε_k→0for ε_k=x_k-x~* and Ka function only of the derivatives of f at x~*.The methods to be discussed require one function evaluation and several 1-orderderivative evaluations.They have the advantage when the derivative f^(?) can be ob-
文摘Let f*g (z) be the convolution or Hadamard product of two functiom f(z) and g(z), that is, if f (z) =z+sum from n=2 to ∞a_nz^n and g(z) =z+sum from n=2 to ∞b_n z_n, then f*g(z)=z+sum from n=2 to ∞a_n b_n z^n (1) Let T denote the class of functions of the
