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Previous attempts to combine Hartree–Fock theory with local density‐functional theory have been unsuccessful in applications to molecular bonding. We derive a new coupling of these two theories that maintains their simplicity and computational efficiency, and yet greatly improves their predictive power. Very encouraging results of tests on atomization energies, ionization potentials, and proton affinities are reported, and the potential for future development is discussed.

A New Mixing of Hartree-Fock and Local Density-Functional Theories

We highlight the trends leading to the increased appeal of using hybrid multicore+GPU systems for high performance computing. We present a set of techniques that can be used to develop efficient dense linear algebra algorithms for these systems. We illustrate the main ideas with the development of a hybrid LU factorization algorithm where we split the computation over a multicore and a graphics processor, and use particular techniques to reduce the amount of pivoting and communication between the hybrid components. This results in an efficient algorithm with balanced use of a multicore processor and a graphics processor.

http://www.netlib.org/utk/people/JackDongarra/PAPERS/lawn210.pdf

Towards dense linear algebra for hybrid GPU accelerated manycore systems

The BLAS-like Library Instantiation Software (BLIS) framework is a new infrastructure for rapidly instantiating Basic Linear Algebra Subprograms (BLAS) functionality. Its fundamental innovation is that virtually all computation within level-2 (matrix-vector) and level-3 (matrix-matrix) BLAS operations can be expressed and optimized in terms of very simple kernels. While others have had similar insights, BLIS reduces the necessary kernels to what we believe is the simplest set that still supports the high performance that the computational science community demands. Higher-level framework code is generalized and implemented in ISO C99 so that it can be reused and/or reparameterized for different operations (and different architectures) with little to no modification. Inserting high-performance kernels into the framework facilitates the immediate optimization of any BLAS-like operations which are cast in terms of these kernels, and thus the framework acts as a productivity multiplier. Users of BLAS-dependent applications are given a choice of using the traditional Fortran-77 BLAS interface, a generalized C interface, or any other higher level interface that builds upon this latter API. Preliminary performance of level-2 and level-3 operations is observed to be competitive with two mature open source libraries (OpenBLAS and ATLAS) as well as an established commercial product (Intel MKL).

/pdf/blis-a-framework-for-rapidly-instantiating-blas-3bgy3lyeew.pdf

BLIS: A Framework for Rapidly Instantiating BLAS Functionality

Parallelizing dense matrix computations to distributed memory architectures is a well-studied subject and generally considered to be among the best understood domains of parallel computing. Two packages, developed in the mid 1990s, still enjoy regular use: ScaLAPACK and PLAPACK. With the advent of many-core architectures, which may very well take the shape of distributed memory architectures within a single processor, these packages must be revisited since the traditional MPI-based approaches will likely need to be extended. Thus, this is a good time to review lessons learned since the introduction of these two packages and to propose a simple yet effective alternative. Preliminary performance results show the new solution achieves competitive, if not superior, performance on large clusters.

/pdf/elemental-a-new-framework-for-distributed-memory-dense-1cewzjr7ed.pdf

Elemental: A New Framework for Distributed Memory Dense Matrix Computations

In physics, it is sometimes desirable to compute the so-called density of states (DOS), also known as the spectral density, of a real symmetric matrix $A$. The spectral density can be viewed as a probability density distribution that measures the likelihood of finding eigenvalues near some point on the real line. The most straightforward way to obtain this density is to compute all eigenvalues of $A$, but this approach is generally costly and wasteful, especially for matrices of large dimension. There exist alternative methods that allow us to estimate the spectral density function at much lower cost. The major computational cost of these methods is in multiplying $A$ with a number of vectors, which makes them appealing for large-scale problems where products of the matrix $A$ with arbitrary vectors are relatively inexpensive. This article defines the problem of estimating the spectral density carefully and discusses how to measure the accuracy of an approximate spectral density. It then surveys a few kno...

pdf/approximating-spectral-densities-of-large-matrices-1y0t9irzde.pdf

Approximating Spectral Densities of Large Matrices

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References

A New Mixing of Hartree-Fock and Local Density-Functional Theories

Towards dense linear algebra for hybrid GPU accelerated manycore systems

BLIS: A Framework for Rapidly Instantiating BLAS Functionality

Elemental: A New Framework for Distributed Memory Dense Matrix Computations

Approximating Spectral Densities of Large Matrices