Recent work on eigenvalues and eigenvectors for tensors of order m >= 3 has been motivated by applications in blind source separation, magnetic resonance imaging, molecular conformation, and more. In this paper, we consider methods for computing real symmetric-tensor eigenpairs of the form Ax^{m-1} = \lambda x subject to ||x||=1, which is closely related to optimal rank-1 approximation of a symmetric tensor. Our contribution is a shifted symmetric higher-order power method (SS-HOPM), which we show is guaranteed to converge to a tensor eigenpair. SS-HOPM can be viewed as a generalization of the power iteration method for matrices or of the symmetric higher-order power method. Additionally, using fixed point analysis, we can characterize exactly which eigenpairs can and cannot be found by the method. Numerical examples are presented, including examples from an extension of the method to finding complex eigenpairs

Several tensor eigenpair definitions have been put forth in the past decade, but these can all be unified under generalized tensor eigenpair framework, introduced by Chang, Pearson, and Zhang (2009). Given mth-order, n-dimensional real-valued symmetric tensors A and B, the goal is to find λ ∈ R and x ∈ R n , x = 0 such that Ax m−1 = λBx m−1 . Different choices for B yield different versions of the tensor eigenvalue problem. We present our generalized eigenproblem adaptive power (GEAP) method for solving the problem, which is an extension of the shifted symmetric higher-order power method (SS-HOPM) for finding Z-eigenpairs. A major drawback of SS-HOPM was that its performance depended in choosing an appropriate shift, but our GEAP method also includes an adaptive method for choosing the shift automatically.

Efficient design of hardware and software for large-scale parallel execution requires detailed understanding of the interactions between the application, computer, and network. The authors have developed a macro-scale simulator (SST/macro) that permits the coarse-grained study of distributed-memory applications. In the presented work, applications using the Message Passing Interface (MPI) are simulated; however, the simulator is designed to allow inclusion of other programming models. The simulator is driven from either a trace file or a skeleton application. Trace files can be either a standard format (Open Trace Format) or a more detailed custom format (DUMPI). The simulator architecture is modular, allowing it to easily be extended with additional network models, trace file formats, and more detailed processor models. This paper describes the design of the simulator, provides performance results, and presents studies showing how application performance is affected by machine characteristics.

Efficient design of hardware and software for large-scale parallel execution requires detailed understanding of the interactions between the application, computer, and network. The authors have developed a macro-scale simulator (SST/macro) that permits the coarse-grained study of distributed-memory applications. In the presented work, applications using the Message Passing Interface (MPI) are simulated; however, the simulator is designed to allow inclusion of other programming models. The simulator is driven from either a trace file or a skeleton application. Trace files can be either a standard format (Open Trace Format) or a more detailed custom format (DUMPI). The simulator architecture is modular, allowing it to easily be extended with additional network models, trace file formats, and more detailed processor models. This paper describes the design of the simulator, provides performance results, and presents studies showing how application performance is affected by machine characteristics.

Application resilience is a key challenge that has to be addressed to realize the exascale vision. Online recovery, even when it involves all processes, can dramatically reduce the overhead of failures as compared to the more traditional approach where the job is terminated and restarted from the last checkpoint. In this paper we explore how local recovery can be used for certain classes of applications to further reduce overheads due to resilience. Specifically we develop programming support and scalable runtime mechanisms to enable online and transparent local recovery for stencil-based parallel applications on current leadership class systems. We also show how multiple independent failures can be masked to effectively reduce the impact on the total time to solution. We integrate these mechanisms with the S3D combustion simulation, and experimentally demonstrate (using the Titan Cray-XK7 system at ORNL) the ability to tolerate high failure rates (i.e., node failures every 5 seconds) with low overhead while sustaining performance, at scales up to 262144 cores.