Heterogeneous computing system with both CPUs and GPUs has become a class of widely used hardware architecture in supercomputers. As heterogeneous systems delivering higher computational performance, they are being built with an increasing number of complex components. This is anticipated that these systems will be more susceptible to hardware faults with higher power consumption. Numerical linear algebra libraries are used in a wide spectrum of high-performance scientific applications. Among numerical linear algebra operations, one-sided matrix decompositions can sometimes take a large portion of execution time or even dominate the whole scientific application execution. Due to the computational characteristic of one-sided matrix decompositions, they are very suitable for computation platforms such as heterogeneous systems with CPUs and GPUs. Many works have been done to implement and optimize one-sided matrix decompositions on heterogeneous systems with CPUs and GPUs. However, it is challenging to enable stable and high performance one-sided matrix decompositions running on computing platforms that are unreliable and high energy consumption. So, in this thesis, we aim to develop novel fault tolerance and energy efficiency optimizations for one-sided matrix decompositions on heterogeneous systems with CPUs and GPUs.

To improve reliability and energy efficiency, extensive researches have been done on developing and optimizing fault tolerance methods and energy-saving strategies for one-sided matrix decompositions. However, current designs still have several limitations: (1) Little has been done on developing and optimizing fault tolerance method for one-sided matrix decompositions on heterogeneous systems with GPUs; (2) Limited by the protection coverage and strength, existing fault tolerance works provide insufficient protection when applied to one-sided matrix decompositions on heterogeneous systems with GPUs; (3) Lack the knowledge of algorithms, existing system level energy saving solutions cannot achieve the optimal energy savings due to potentially inaccurate and high-cost workload prediction they rely on when they are used in one-sided matrix decompositions; (4) It is challenging to apply both fault tolerance techniques and energy saving strategies to one-side matrix decompositions at the same time given that their current designs are not naturally compatible with each other.

To address the first problem, based on the original (Algorithm Based Fault Tolerance) ABFT, we develop the first ABFT for matrix decomposition on heterogeneous systems with GPUs together with the novel storage errors protection and several optimization techniques specifically for GPUs. As for the second problem, we design a novel checksum scheme for ABFT that allows data stored in matrices to be encoded in two dimensions. This stronger checksum encoding mechanism enables much stronger protection including enhanced error propagation protection. In addition, we introduce a more efficient checking scheme. By prioritizing the checksum verification according to the sensitivity of matrix operations to soft errors with optimized checksum verification kernel for GPUs, we can achieve strong protect to matrix decompositions with comparable overhead. For the third problem, to improve energy efficiency for one-sided matrix decompositions, we introduce an algorithm-based energy-saving approach designed to maximize energy savings by utilizing algorithmic characteristics. Our approach can predict program execution behavior much more accurately, which is difficult for system level solutions for applications with variable execution characteristics. Experiments show that our approach can lead to much higher energy saving than existing works. Finally, for the fourth problem, we propose a novel energy saving approach for one-sided matrix decompositions on heterogeneous systems with GPUs. It allows energy saving strategies and fault tolerance techniques to be enabled at the same time without brings performance impact or extra energy cost.