A Shamanskiĭ-like acceleration scheme for nonlinear equations at singular roots

C. T. Kelley
1986 Mathematics of Computation  
A variation of the Shamanskii method is used to obtain a superlinearly convergent method for a class of nonlinear equations having singular Fréchet derivative at the root. The cost of a superlinear step is one derivative evaluation and two function evaluations.
doi:10.1090/s0025-5718-1986-0856706-4 fatcat:gzfziklawnbrrprx3ykwzt5uba