A globally convergent ball Stirling method Original Research Article

A STIRLING method for the solution of a system of equations can be viewed as a combination of the method of successive substitution and Newton method. In [Acqu. Math. 12 (1975) 12], the author established the convergence of Stirling method in Banach spaces. In contrast to the point Newton method, the ball Newton method, developed in [SIAM J. Numer. Anal. 18 (1981) 988] and further modified in [Soochow J. Math. 19 (1993) 199], generates a sequence of n-dimensional balls of diminishing radii with the property that each ball contains the root of the operator in question rather than a new approximating point. This paper establishes the ball Stirling method in analogy with ball Newton method, as an effective tool for solving various equations.