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There are many works devoted to improving the matrix product computation, as it is used in a wide variety of scientific applications arising from many different fields. In this work, we propose alternative data distribution policies and ...

High-Performance Computing (HPC) systems today are gradually increasing in size and complexity due to the correspondent demand for ever-increasing computing needs, requiring more complicated tasks and higher accuracy. The growing energy needs of HPC ...

Solution of the symmetric definite generalized eigenvalue problem (GEP) $A\mathbf{x}=\lambda B\mathbf{x}$ lies at the heart of many scientific computations like electronic structure calculations. The standard algorithm for this problem consists of two parts, namely, ...

In high-performance computing, the general matrix-matrix multiplication (xGEMM) routine is the core of the Level 3 BLAS kernel for effective matrix-matrix multiplication operations. The performance of parallel xGEMM (PxGEMM) is significantly ...

This paper introduces a high performance implementation of the Zolo-SVD algorithm on distributed memory systems, which is based on the polar decomposition (PD) algorithm via the Zolotarev’s function (Zolo-PD), originally proposed by ...

In this paper, we propose an efficient divide-and-conquer (DC) algorithm for symmetric tridiagonal matrices based on ScaLAPACK and the hierarchically semiseparable (HSS) matrices. HSS is an important type of rank-structured matrices. ...

This paper studies the resilience of a two-sided factorization and presents a generic algorithm-based approach capable of making two-sided factorizations resilient. We establish the theoretical proof of the correctness and the numerical stability of the ...

We present a new distributed programming extension of the R programming language. By tightly coupling R to the well-known ScaLAPACK and MPI libraries, we are able to achieve highly scalable implementations of common statistical methods, allowing the ...

To obtain accurate and reliable estimations of the major lithological properties of the rock within a studied volume, geophysics uses the joint information provided by different geophysical datasets (e.g. gravimetric, magnetic, seismic). Representation ...

Excessive energy consumption has become one of the major challenges in high performance computing. Reducing the energy consumption of frequently used high performance computing applications not only saves the energy cost but also reduces the greenhouse ...

Partitioned Global Address Space (PGAS) languages offer programmers a shared memory view that increases their productivity and allow locality exploitation to obtain good performance on current large-scale distributed memory systems. UPCBLAS is a ...

The ScaLAPACK library contains a pair of routines for solving banded linear systems which are strictly diagonally dominant by rows. Mathematically, the algorithm is complete block cyclic reduction corresponding to a particular block partitioning of the ...

ScaLAPACK contains a pair of routines for solving systems which are narrow banded and diagonally dominant by rows. Mathematically, the algorithm is block cyclic reduction. The ScaLAPACK implementation can be improved using incomplete, rather than ...

The (sequential) algorithm of Multiple Relatively Robust Representations, MRRR, is a more efficient variant of inverse iteration that does not require reorthogonalization. It solves the eigenproblem of an unreduced symmetric tridiagonal matrix T ∈ R^{n × ...}

In many high performance engineering and scientific applications there is a need to use parallel software libraries. Researchers behind these applications find it difficult to understand the interfaces to these libraries because they carry arguments ...

We present parallel algorithms for triangular periodic Sylves-ter-type matrix equations, conceptually being the third step of a periodic Bartels---Stewart-like solution method for general periodic Sylvester-type matrix equations based on variants of the ...

This paper presents a package, called Heterogeneous PBLAS (HeteroPBLAS), which is built on top of PBLAS and provides optimized parallel basic linear algebra subprograms for heterogeneous computational clusters. We present the user interface and the ...

This paper discusses the design and the implementation of the LU factorization routines included in the Heterogeneous ScaLAPACK library, which is built on top of ScaLAPACK. These routines are used in the factorization and solution of a dense system of ...

Jack Dongarra, a leader of the high-performance computing community, is cocreator of mathematical software packages including EISPACK, LINPACK, LAPACK, and ScaLAPACK. He is also a University Distinguished Professor at the University of Tennessee.

In this paper, we proposed a unified framework and tried to address the optimal block size selection problem for parallel blocked LU and QR factorization algorithm used in ScaLAPACK package, since they use two dimensional block cyclic data distribution ...