Advantageously, embodiments of the invention provide techniques for determining dependency relationships between matrix supernodes by storing a list of dependencies for each supernode in a data structure and augmenting this list as needed when a column is moved from one supernode to another while factorizing a series Ai of symmetric matrices. As iterating over all supernodes to determine which supernodes a given supernode depends on at the beginning of each factorization adds significant overhead to the computation, embodiments described above maintains a supernode dependency data structure used for each successive factorization, greatly reducing the overhead of the dependency determination.