What is convergent improvement?
If you have a good single cross (A X B), and you know the vigour is the result of the dominance of growth factors, back-cross it several generations to A, selecting for qualities of B that are lacking in A. After two or more generations of back-crossing and selecting, IBLs are produced. Do the same for B. After improved A and B are obtained, they are tested in crosses and compared to the original (A X B).
Multiple convergence is improving an inbred by convergence of gametes from different sources. If A is a very desirable inbred in crosses, it can be modified in two seperate back-cross programs , with the idea that the improved inbreds will be vigourous enough to use as the male parent of a double-cross.