Solving tridiagonal Toeplitz systems of linear equations on GPU‐accelerated computers

Dmitruk, Beata; Stpiczyński, Przemysław

doi:10.1002/cpe.6449

Cited by 2 publications

(3 citation statements)

References 23 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Note that the prefix x in function names indicates the precision TA B L E 4 Relative error of all considered methods (double precision). 3.3e-10 1.2e-11 0.0e-00 0.0e-00 0.0e-00 0.0e-00 0.0e-00 0.0e-00 2 30 2 4 4.2e-10 3.5e-11 0.0e-00 0.0e-00 0.0e-00 0.0e-00 0.0e-00 0.0e-00 TA B L E 5 Relative error of all considered methods (single and mixed precision). used (i.e., D for double, F for single, respectively).…”

Section: Results Of Experimentsmentioning

confidence: 99%

“…However, if summation is only a part of implemented problem, for example when summed numerical values are computed during summation using a more complicated procedure, then the use of multiple processors can be profitable even for smaller problem sizes. In the future, we plan to implement several algorithms for solving such problems (numerical integration, solving ordinary differential equations and tridiagonal systems of linear equations 30 ) in order to examine how the use of parallel and vectorized compensated summation algorithms affects accuracy and performance.…”

Section: Discussionmentioning

confidence: 99%

See 1 more Smart Citation

Improving accuracy of summation using parallel vectorized Kahan's and Gill‐Møller algorithms

Dmitruk

Stpiczyński

2023

Concurrency and Computation

Self Cite

View full text Add to dashboard Cite

The aim of this paper is to show that Kahan's and Gill‐Møller compensated summation algorithms that allow to achieve high accuracy of summing long sequences of floating‐point numbers can be efficiently vectorized and parallelized using Intel AVX‐512 intrinsics together with OpenMP constructs in order to utilize SIMD extension of modern multicore processors. Numerical experiments show that the new implementations of the algorithms achieve much better accuracy than ordinary summation in both double and single precision and their performance is comparable with the performance of the ordinary summation algorithm optimized automatically. The vectorized Gill‐Møller algorithm is faster than the vectorized Kahan's algorithm. However, in case of single precision, the accuracy of the Gill‐Møller algorithm is worse than Kahan's but it can be fixed by the use of mixed‐precision. Then the accuracy of both compensated summation algorithms is the same and the Gill‐Møller algorithm is still faster than Kahan's.

show abstract

Section: Results Of Experimentsmentioning

confidence: 99%

Section: Discussionmentioning

confidence: 99%

Improving accuracy of summation using parallel vectorized Kahan's and Gill‐Møller algorithms

Dmitruk

Stpiczyński

2023

Concurrency and Computation

Self Cite

View full text Add to dashboard Cite

show abstract

“…Dmitruk et al 3 show how the OpenACC standard can be efficiently used to implement solvers for tridiagonal Toeplitz systems of linear equations for a variety of modern GPU‐accelerated and multicore architectures. Two parallel algorithms are studied concerning particular assumptions about coefficient matrices.…”

Section: Accepted Papers For the Special Issue: Summarymentioning

confidence: 99%

Algorithmic and software development advances for next‐generation heterogeneous platforms

Wyrzykowski

Ciorba

2022

Concurrency and Computation

View full text Add to dashboard Cite

Heterogeneity is emerging as one of the most profound and challenging characteristics of today's and tomorrow's parallel and distributed computing environments, presenting new and exciting opportunities for their development. Most modern computing systems are heterogeneous, either for organic reasons because components grew independently, as is the case of desktop grids, by design to leverage the strength of specific hardware, as is the case of accelerated systems, or both. The impact of heterogeneity on all forms of parallel and distributed computing is increasing rapidly.Traditional algorithms, programming environments, and tools designed for legacy homogeneous systems will at best achieve a small fraction of the efficiency and the potential performance expected from parallel computing in tomorrow's highly diversified and mixed architectures. Innovative ideas, fresh models, novel algorithms, and other specialized or unified programming environments and tools are needed to efficiently use these new and increasingly diverse computing systems-for accelerating scientific discovery and impactful innovation.The International Workshop on Algorithms, Models and Tools for Parallel Computing on Heterogeneous Platforms (HeteroPar) has been the premier forum over the last 20 years, bringing together researchers to discuss these challenges and the solutions. The wide range of topics includes achieving performance portability on heterogeneous architectures, advances in software environments that facilitate efficient use of heterogeneous systems, performance and energy optimization of numerical and machine learning algorithms on heterogeneous platforms, to name a few.The works presented at the HeteroPar'2020 workshop covered topics clearly exhibiting the significance and growth of the heterogeneous computing field. However, one general trend is apparent: the broad adoption of Graphics Processing Units (GPU) accelerators. Over the last decade, GPUs have been established as the main powerhouse in leadership supercomputers and an invaluable component to accelerate computations for a vast spectrum of applications-from numerical linear algebra libraries powering computational science to various machine learning workloads. This trend is evidenced by the increasing number of GPU-related publications submitted to HeterPar and supported by growing diversity within the GPU world, where AMD accelerator architectures start to compete with Nvidia's comprehensive solutions, along with the third GPU accelerator option-from Intel-available soon.This special issue of Concurrency and Computation: Practice and Experience contains six selected papers from the HeteroPar'2020 workshop.We hope you find them interesting and stimulating new ideas and future advancements for next-generation heterogeneous platforms.

show abstract

Solving tridiagonal Toeplitz systems of linear equations on GPU‐accelerated computers

Cited by 2 publications

References 23 publications

Improving accuracy of summation using parallel vectorized Kahan's and Gill‐Møller algorithms

Improving accuracy of summation using parallel vectorized Kahan's and Gill‐Møller algorithms

Algorithmic and software development advances for next‐generation heterogeneous platforms

Contact Info

Product

Resources

About