منابع مشابه
Block-Cyclic Dense Linear Algebra
Block{cyclic order elimination algorithms for LU and QR factorization and solve routines are described for distributed memory architectures with processing nodes conngured as two{dimensional arrays of arbitrary shape. The cyclic order elimination together with a consecutive data allocation yields good load{balance for both the factorization and solution phases for the solution of dense systems ...
متن کاملDense Linear Algebra Pattern
The pivotal problem in computational linear algebra is how to balance data access costs with the cost of computation. Given the disparity between memory and CPU speeds, it is critical to maximize the amount of computation carried out for each item of data accessed from memory. For problems for which the systems of equations associated with a problem are dense (i.e. they contain mostly non-zero ...
متن کاملAutotuning dense linear algebra libraries on GPUs
As GPUs are quickly evolving in complexity, tuning numerical libraries for them is becoming more challenging. We present an autotuning approach in the area of dense linear algebra (DLA) libraries for GPUs. The MAGMA library is used to demonstrate the techniques and their effect on performance and portability across hardware systems. We show that, figuratively speaking, our autotuning approach f...
متن کاملLooking back at dense linear algebra software
Over the years, computational physics and chemistry served as an ongoing source of problems that demanded the ever increasing performance from hardware as well as the software that ran on top of it. Most of these problems could be translated into solutions for systems of linear equations: the very topic of numerical linear algebra. Seemingly then, a set of efficient linear solvers could be solv...
متن کاملRecent Developments in Dense Numerical Linear Algebra
We survey recent developments in dense numerical linear algebra, covering linear systems, least squares problems and eigenproblems. Topics considered include the design and analysis of block, partitioned and parallel algorithms, condition number estimation, componentwise error analysis, and the computation of practical error bounds. Frequent reference is made to LAPACK, the state of the art pac...
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ژورنال
عنوان ژورنال: SIAM Journal on Scientific Computing
سال: 1993
ISSN: 1064-8275,1095-7197
DOI: 10.1137/0914075