Abstract: 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.

Abstract: 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.

Abstract: A method, system and computer program product to improve multiplication of a vector by a product of elementary matrices. The method includes, for example, receiving an input vector and determining, by at least one computer processor, which intermediate resultants of a matrix vector product between the input vector and a plurality of elementary matrices can be performed in parallel. At least some of the intermediate resultants may be calculated in parallel by a plurality of computer processors if they are not dependent on the pending product resultant of the input vector and one or more of the elementary matrices.