Newton’s Method for Singular Problems when the Dimension of the Null Space is $>1$

A theorem is proved concerning the convergence of Newton’s method when the dimension of the null space of the Jacobian matrix is $>1$. It improves on previous results of Decker and Kelley (SIAM J. Numer. Anal., 17 (1980), pp. 66’70) and Reddien (Comput. Math. Appl., 5 (1980), pp. 79’86).