Tridiagonal solvers are important building blocks for a wide range of scientic 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 eciently 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 suers 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.