This paper describes the design and implementation of three core factorization routines—LU, QR, and Cholesky—included in the out-of-core extension of ScaLAPACK. These routines allow the factorization and solution of a dense system that is too large to fit entirely in physical memory. The full matrix is stored on disk and the factorization routines transfer sub-matrice panels into memory. The ‘l...

A 'new' Lutheran-related antibody, named anti-Lu14, reacts with approximately 2.4% of random bloods. Red cells of the rare Lu:-8 phenotype are Lu:14. The data indicate, with a high probability, that the Lu 14 antigen is a product of an allele of Lu8 and that Lu14 and Lu8 comprise a third pair of alleles at the Lutheran locus. Red cells of the original Sw (a+) propositus are Lu:14. By coincidenc...

SUMMARY Efficient numerical wave modelling is essential for imaging methods such as reverse-time migration (RTM) and full waveform inversion (FWI). In 2D, frequency-domain modelling with LU factorization as a direct solver can outperform time-domain methods by one order. For 3-D problems, the computational complexity of the LU factorization as well as its memory requirements are a disadvantage ...

We combine the idea of the direct LU factorization with the idea of the pivoting strategy in the usual Gaussian elimination and show that two so-called total scaled and total pivoting strategies can be employed in addition to the traditional pivoting strategies: partial scaled, partial, and direct diagonal. In this paper we o er a general LU factorization with total scaled pivoting algorithm fr...

HPF coding examples of practical scientific algorithms are examined in detail, with the idea that on these simple but non-trivial examples, we can fairly well understand issues related to different data distributions, different parallel constructs, and different programming styles (static vs dynamic allocations). Coding examples include 2D stencils solution of PDEs, N-body problem, LU factoriza...

In this paper the accuracy of LU factorization of tridiagonal matrices without pivoting is considered. Two types of componentwise condition numbers for the L and U factors of tridiadonal matrices are presented and compared. One type is a condition number with respect to small relative perturbations of each entry of the matrix. The other type is a condition number with respect to small component...

Several driving forces have recently brought about significant advances in the field of configurable computing. They have also enabled parallel processing within a single field-programmable gate array (FPGA) chip. The ever-increasing complexity of application algorithms and the supercomputing crisis have made this new parallel-processing approach more important and pertinent. Its cost-effective...

The traditional approach to the parallelization of linear algebra algorithms such as matrix multiplication and LU factorization calls for static allocation of matrix blocks to processing elements (PEs). Such algorithms suffer from two drawbacks : they are very sensitive to load imbalances between PEs and they make it difficult to take advantage of pipelining opportunities. This paper describes ...

There has been considerable experimental and theoretical interest in semi-inclusive hadron production in deep inelastic scattering (SIDIS) processes. For example, by studying the polarized and unpolarized SIDIS, one will be able to identify the sea quark distribution and polarization in nucleon, and the experimental results from the HERMES collaboration have revealed nontrivial sea structure in...

We investigate several ways to improve the performance of sparse LU factorization with partial pivoting, as used to solve unsymmetric linear systems. We introduce the notion of unsymmetric supernodes to perform most of the numerical computation in dense matrix kernels. We introduce unsymmetric supernode-panel updates and two-dimensional data partitioning to better exploit the memory hierarchy. ...