F11DNF Note: before using this routine, please read the Users' Note for your implementation to check the interpretation of bold italicised terms and other implementation-dependent details. 1 Purpose F11DNF computes an incomplete LU factorization of a complex sparse non-Hermitian matrix, represented in coordinate storage format. This factorization may be used as a preconditioner in combination w...

Static symbolic factorization coupled with supernode partitioning and asynchronous computation scheduling can achieve high giga op rates for parallel sparse LU factorization with partial pivoting This paper studies properties of elimination forests and uses them to optimize supernode partitioning amalgamation and execution scheduling It also proposes supernodal matrix multiplication to speed up...

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The perfect 1-factorization conjecture by A. Kotzig [7] asserts the existence of a 1-factorization of a complete graph K2n in which any two 1-factors induce a Hamiltonian cycle. This conjecture is one of the prominent open problems in graph theory. Apart from its theoretical significance it has a number of applications, particularly in designing topologies for wireless communication. Recently, ...

This paper analyzes dropping strategies in a multilevel incomplete LU decomposition context and presents a few of strategies for obtaining related ILUs with enhanced robustness. The analysis shows that the Incomplete LU factorization resulting from dropping small entries in Gaussian elimination produces a good preconditioner when the inverses of these factors have norms that are not too large. ...

This paper introduces the hierarchical interpolative factorization for integral equations (HIF-IE) associated with elliptic problems in two and three dimensions. This factorization takes the form of an approximate generalized LU decomposition that permits the efficient application of the discretized operator and its inverse. HIF-IE is based on the recursive skeletonization algorithm but incorpo...

This paper gives an algorithm for solving linear systems, using a randomized version of incomplete LU factorization together with iterative improvement. The factorization uses Gaussian elimination with partial pivoting, and preserves sparsity during factorization by randomized rounding of the entries. The resulting approximate factorization is then applied to estimate the solution. This simple ...

We present an algebraic structured preconditioner for the iterative solution of large sparse linear systems. The preconditioner is based on a multifrontal variant of sparse LU factorization used with nested dissection ordering. Multifrontal factorization amounts to a partial factorization of a sequence of logically dense frontal matrices, and the preconditioner is obtained if structured factori...

This research is to provide a solution of one-way ANOVA without using transformation when variances are heteroscedastic and group sizes are unequal. Parametric boothstrap test (Krishnamoorthy, Lu, & Mathew, 2007) has been shown to be competitive with many other methods when testing the equality of group means. We extend the parametric bootstrap algorithm to a multiple comparison procedure. Simu...

To solve sparse linear systems multifrontal methods rely on dense partial LU decompositions of so-called frontal matrices; we consider a parallel, asynchronous setting in which several frontal matrices can be factored simultaneously. In this context, to address performance and scalability issues of acyclic pipelined asynchronous factorization kernels, we study models to revisit properties of le...