In this technical report we study different parallel graph coloring algorithms and their application to the incomplete-LU factorization. We implement graph coloring based on different heuristics and showcase their performance on the GPU. We also present a comprehensive comparison of level-scheduling and graph coloring approaches for the incomplete-LU factorization and triangular solve. We discu...

In this paper we consider the computation of an eigenvalue and corresponding eigenvector of a large sparse Hermitian positive definite matrix using inexact inverse iteration with a fixed shift. For such problems the large sparse linear systems arising at each iteration are often solved approximately by means of symmetrically preconditioned MINRES. We consider preconditioners based on the incomp...

Parallel sparse direct solvers are now able to solve efficiently real-life three-dimensional problems having in the order of several millions of equations. They are, however, constrained by prohibitive memory requirements. Iterative methods on the other hand require much less memory, but they often fail to solve ill-conditioned systems. We propose an hybrid direct-iterative method which aims at...

Iterative methods are often suitable for solving least-squares problems minkAx bk2 , where A 2 R n is large and sparse. The use of the conjugate gradient method with a nonsingular square submatrix A1 2 R n of A as preconditioner was first suggested by Läuchli in 1961. This conjugate gradient method has recently been extended by Yuan to generalized least-squares problems. In this paper we consid...

Efficient cloth simulation is an important problem for interactive applications that involve virtual humans, such as computer games. A common aspect of many methods that have been developed to simulate cloth is a linear system of equations, which is commonly solved using conjugate gradient or multi-grid approaches. In this paper, we introduce to the computer gaming community a recently proposed...

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This paper introduces a new sweeping preconditioner for the iterative solution of the variable coefficient Helmholtz equation in two and three dimensions. The algorithms follow the general structure of constructing an approximate LDLt factorization by eliminating the unknowns layer by layer starting from an absorbing layer or boundary condition. The central idea of this paper is to approximate ...

A Class of Splitting Preconditioners for the iterative solution of Linear Systems arising from Interior Point Methods for Linear Programming Problems needs to find a base by a sophisticated process based in a lying rectangular LU factorization, that involves reordering columns many times until certain conditions are satisfied. At the same time, it is necessary to prevent excessive fill-in in L ...

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...