Q-quadratic Convergence for A Subclass of Nonlinear ABS Algorithms

The subclass of nonlinear ABS algorithms corresponding to the first class of voyevodin method is considered and its Q-quadratic covergence is proved. Particularly, ths Q-quadratic convergnce is derived from the subclass corresponding to the conjugate direction methods and the condition of the superlinear convergence theorem given by Abaffy J. is clarified.