Scalable parallel tridiagonal algorithms with diagonal pivoting and their optimization for many-core architectures

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.

Name thesis:degree_name

M.S.

Level thesis:degree_level

Thesis

Discipline thesis:degree_discipline

Electrical & Computer Engr

Grantor

University of Illinois at Urbana-Champaign

Year dc:date

2014

Author dc:creator

• Chang, Li-Wen

Contributors dc:contributor

• Hwu, Wen-Mei W.

• 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

Statement dc:rights

• Copyright 2014 Li-Wen Chang

Language dc:language

en

Handle dc:identifier

http://hdl.handle.net/2142/50588

OAI identifier oai:identifier

oai:www.ideals.illinois.edu:2142/50588