We find that the only algorithm that solves all the test cases with a 100 % success rate is the outer fixed-point algorithm. The inner fixed-point algorithm is less robust and fails to solve the iron-chromium test 1.62 % of the time. The weakest algorithm is the full Newton algorithm, which fails at a 0.05 % rate for gallic acid test and at a 91.35 % rate for the iron-chromium test.
Table 5: Failure ratio after 1,000 iterations