The central problem in the determination of protein structures form x-ray diffraction dada (x-ray crystallography) corresponds to a phase retrieval problem with undersampled amplitude data. Algorithms for this problem that have an increased radius of convergence have the potential for reducing the amount of experimental work, and cost, involved in determining protein structures. We describe such an algorithm. Application of the algorithm to a simulated crystallographic problem shows that it converges to the correct solution, with no initial phase information, where currently used algorithms fail. The results lend support to the possibility of ab initio phasing in protein crystallography.