1. A computer-implemented method for maintaining dependencies among supernodes during repeated matrix factorizations of sparse matrices, comprising: determining a set of supernodes of the sparse matrices; for each determined supernode, determining a set of zero or more supernodes on which the supernode depends; during one or more successive rounds of factorizing the sparse matrices: deferring at least a column assigned to a first one of the supernodes to a second one of the supernodes, identifying one or more supernodes on which the first supernode depends, and updating the set of supernodes on which the second supernode depends to include one or more of the supernodes on which the first supernode depends.