We present a fast hybrid solver for dense linear systems based on LU factorization. To achieve good performance, we avoid pivoting by using random butterfly transformations for which we developed efficient implementations on heterogeneous architectures. We used both Graphics Processing Units and Intel Xeon Phi as accelerators. The performance results show that the pre-processing due to randomiz...

We discuss and compare two greedy algorithms, that compute discrete versions of Fekete-like points for multivariate compact sets by basic tools of numerical linear algebra. The first gives the so-called “Approximate Fekete Points” by QR factorization with column pivoting of Vandermonde-like matrices. The second computes Discrete Leja Points by LU factorization with row pivoting. Moreover, we st...

This work studies the use of visual semantic representations to align entities in heterogeneous knowledge graphs (KGs). Images are natural components many existing KGs. By combining with other auxiliary information, we show that proposed new approach, EVA, creates a holistic entity representation provides strong signals for cross-graph alignment. Besides, previous alignment methods require huma...

Positioning of the mitotic spindle is crucial for proper cell division. In the budding yeast Saccharomyces cerevisiae, two mechanisms contribute to spindle positioning. In the Kar9 pathway, astral microtubules emanating from the daughter-bound spindle pole body interact via the linker protein Kar9 with the myosin Myo2, which moves the microtubule along the actin cables towards the neck. In the ...

Incomplete factorization is one of the most effective general-purpose preconditioning methods for Krylov subspace solvers for large sparse systems of linear equations. Two techniques for enhancing the robustness and performance of incomplete LU factorization for sparse unsymmetric systems are described. A block incomplete factorization algorithm based on the Crout variation of LU factorization ...

We report on an extensive experiment to compare an iterative solver preconditioned by several versions of incomplete LU factorization with a sparse direct solver using LU factorization with partial pivoting. Our test suite is 24 nonsymmetric matrices drawn from benchmark sets in the literature. On a few matrices, the best iterative method is more than 5 times as fast and more than 10 times as m...

A 25-year old and somewhat neglected algorithm of Crawford and Moon attempts to determine whether a given Hermitian matrix pair (A,B) is definite by exploring the range of the function f(x) = x(A + iB)x/|x(A + iB)x|, which is a subset of the unit circle. We revisit the algorithm and show that with suitable modifications and careful attention to implementation details it provides a reliable and ...

In this paper, we discuss the use of binary decision diagrams to represent general matrices. We demonstrate that binary decision diagrams are an efficient representation for every special-case matrix in common use, notably sparse matrices. In particular, we demonstrate that for any matrix, the BDD representation can be no larger than the corresponding sparse-matrix representation. Further, the ...