scholarly journals A customized precision format based on mantissa segmentation for accelerating sparse linear algebra

2019 ◽  
Vol 32 (15) ◽  
Author(s):  
Thomas Grützmacher ◽  
Terry Cojean ◽  
Goran Flegar ◽  
Fritz Göbel ◽  
Hartwig Anzt
Keyword(s):  
Linear Algebra ◽  
Sparse Linear Algebra

Memory Optimizations for Sparse Linear Algebra on GPU Hardware

2021 ◽  
Author(s):  
Aaron Walden ◽  
Mohammad Zubair ◽  
Christopher P. Stone ◽  
Eric J. Nielsen
Keyword(s):  
Linear Algebra ◽  
Sparse Linear Algebra ◽  
Memory Optimizations

scholarly journals Scheduling Trees of Malleable Tasks for Sparse Linear Algebra

2015 ◽  
pp. 479-490 ◽  
Author(s):  
Abdou Guermouche ◽  
Loris Marchal ◽  
Bertrand Simon ◽  
Frédéric Vivien
Keyword(s):  
Linear Algebra ◽  
Sparse Linear Algebra

Usability levels for sparse linear algebra components

2008 ◽  
Vol 20 (12) ◽  
pp. 1439-1454 ◽  
Author(s):  
M. Sosonkina ◽  
F. Liu ◽  
R. Bramley
Keyword(s):  
Linear Algebra ◽  
Sparse Linear Algebra

scholarly journals PyTrilinos: Recent Advances in the Python Interface to Trilinos

2012 ◽  
Vol 20 (3) ◽  
pp. 311-325 ◽  
Author(s):  
William F. Spotz
Keyword(s):  
Linear Algebra ◽  
Utility Functions ◽  
Ease Of Use ◽  
Linear Solution ◽  
Dense Linear Algebra ◽  
Multilevel Preconditioners ◽  
Front End ◽  
Nonlinear Solvers ◽  
Sparse Linear Algebra ◽  
Python Package

PyTrilinos is a set of Python interfaces to compiled Trilinos packages. This collection supports serial and parallel dense linear algebra, serial and parallel sparse linear algebra, direct and iterative linear solution techniques, algebraic and multilevel preconditioners, nonlinear solvers and continuation algorithms, eigensolvers and partitioning algorithms. Also included are a variety of related utility functions and classes, including distributed I/O, coloring algorithms and matrix generation. PyTrilinos vector objects are compatible with the popular NumPy Python package. As a Python front end to compiled libraries, PyTrilinos takes advantage of the flexibility and ease of use of Python, and the efficiency of the underlying C++, C and Fortran numerical kernels. This paper covers recent, previously unpublished advances in the PyTrilinos package.

scholarly journals Shift-invert diagonalization of large many-body localizing spin chains

2018 ◽  
Vol 5 (5) ◽  
Author(s):  
Francesca Pietracaprina ◽  
Nicolas Macé ◽  
David J. Luitz ◽  
Fabien Alet
Keyword(s):  
Random Field ◽  
Linear Algebra ◽  
Spin Chain ◽  
Quantum Systems ◽  
Exact Diagonalization ◽  
Spin Chains ◽  
Many Body ◽  
Heisenberg Spin ◽  
Heisenberg Spin Chain ◽  
Sparse Linear Algebra

We provide a pedagogical review on the calculation of highly excited eigenstates of disordered interacting quantum systems which can undergo a many-body localization (MBL) transition, using shift-invert exact diagonalization. We also provide an example code at https://bitbucket.org/dluitz/sinvert_mbl. Through a detailed analysis of the simulational parameters of the random field Heisenberg spin chain, we provide a practical guide on how to perform efficient computations. We present data for mid-spectrum eigenstates of spin chains of sizes up to L=26L=26. This work is also geared towards readers with interest in efficiency of parallel sparse linear algebra techniques that will find a challenging application in the MBL problem.

Sparse Linear Algebra Toolkit for Computational Aerodynamics

2020 ◽  
Author(s):  
Stephen L. Wood ◽  
Kevin Jacobson ◽  
William T. Jones ◽  
William K. Anderson
Keyword(s):  
Linear Algebra ◽  
Computational Aerodynamics ◽  
Sparse Linear Algebra
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