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MFRS : AN ALGORITHM FOR THE STRUCTURED MULTIFRONTAL SOLUTION OF LARGE SPARSE MATRICES VIA RANDOMIZED SAMPLING

This paper presents strategies for the development of an efficient algorithm (MFRS) for the direct solutions of large sparse linear systems. The algorithm is based on a structured multifrontal method with randomized sampling. We propose data structures and access schemes for a type of rank structured matrices, called Hierarchically SemiSeparable (HSS) forms. A data tree structure is used for HSS matrices. Similar strategies are built into a multifrontal factorization method. This yields efficient nested data trees. The fast operations for certain important operations in the factorizations are shown.