Scalable parallel tridiagonal algorithms with diagonal pivoting and their optimization for many-core architectures
Chang, Li-Wen
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https://hdl.handle.net/2142/50588
Description
Title
Scalable parallel tridiagonal algorithms with diagonal pivoting and their optimization for many-core architectures
Author(s)
Chang, Li-Wen
Issue Date
2014-09-16
Director of Research (if dissertation) or Advisor (if thesis)
Hwu, Wen-Mei W.
Department of Study
Electrical & Computer Eng
Discipline
Electrical & Computer Engr
Degree Granting Institution
University of Illinois at Urbana-Champaign
Degree Name
M.S.
Degree Level
Thesis
Keyword(s)
Tridiagonal Solver
SPIKE algorithm
Linear Recurrence
Cyclic Reduction
Diagonal Pivoting
Graphics Processing Unit (GPU) Computing
General Purpose computation on Graphics Processing Units (GPGPU)
Many-core
Abstract
Tridiagonal solvers are important building blocks for a wide range of scientific applications that are commonly performance-sensitive. Recently, many-core architectures, such as GPUs, have become ubiquitous targets for these applications. Therefore, a high-performance general-purpose GPU tridiagonal solver becomes critical. However, no existing GPU tridiagonal solver provides comparable quality of solutions to most common, general-purpose CPU tridiagonal solvers, like Matlab or Intel MKL, due to no pivoting. Meanwhile, conventional pivoting algorithms are sequential and not applicable to GPUs.
In this thesis, we propose three scalable tridiagonal algorithms with diagonal pivoting for better quality of solutions than the state-of-the-art GPU tridiagonal solvers. A SPIKE-Diagonal Pivoting algorithm efficiently partitions the workloads of a tridiagonal solver and provides pivoting in each partition. A Parallel Diagonal Pivoting algorithm transforms the conventional diagonal pivoting algorithm into a parallelizable form which can be solved by high-performance parallel linear recurrence solvers. An Adaptive R-Cyclic Reduction algorithm introduces pivoting into the conventional R-Cyclic Reduction family, which commonly suffers limited quality of solutions due to no applicable pivoting. Our proposed algorithms can provide comparable quality of solutions to CPU tridiagonal solvers, like Matlab or Intel MKL, without compromising the high throughput GPUs provide.
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