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An adaptive shifted power method for computing generalized tensor eigenpairs

SIAM Journal on Matrix Analysis and Applications

Kolda, Tamara G.; Mayo, Jackson M.

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 [J. Math. Anal. Appl., 350 (2009), pp. 416-422]. Given mth-order, n-dimensional realvalued symmetric tensors A and B, the goal is to find λ ε ℝ and x ε ℝn, x ≠= 0 such that Axm-1 = λBxm-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 is that its performance depended on choosing an appropriate shift, but our GEAP method also includes an adaptive method for choosing the shift automatically.

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TYPE Journal Article YEAR 2014
ScopusOSTIDOI

Leveraging Formal Methods and Fuzzing to Verify Security and Reliability Properties of Large-Scale High-Consequence Systems

Ruthruff, Joseph R.; Armstrong, Robert C.; Davis, Benjamin G.; Mayo, Jackson M.; Punnoose, Ratish J.

Formal methods describe a class of system analysis techniques that seek to prove specific properties about analyzed designs, or locate flaws compromising those properties. As an analysis capability,these techniques are the subject of increased interest from both internal and external customers of Sandia National Laboratories. Given this lab's other areas of expertise, Sandia is uniquely positioned to advance the state-of-the-art with respect to several research and application areas within formal methods. This research project was a one-year effort funded by Sandia's CyberSecurity S&T Investment Area in its Laboratory Directed Research & Development program to investigate the opportunities for formal methods to impact Sandia's present mission areas, more fully understand the needs of the research community in the area of formal methods and where Sandia can contribute, and clarify from those potential research paths those that would best advance the mission-area interests of Sandia. The accomplishments from this project reinforce the utility of formal methods in Sandia, particularly in areas relevant to Cyber Security, and set the stage for continued Sandia investments to ensure this capabilityis utilized and advanced within this laboratory to serve the national interest.

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TYPE SAND Report YEAR 2012
OSTIDOI

What then do we do about computer security?

Berg, Michael J.; Davis, Christopher E.; Mayo, Jackson M.; Suppona, Roger A.; Wyss, Gregory D.

This report presents the answers that an informal and unfunded group at SNL provided for questions concerning computer security posed by Jim Gosler, Sandia Fellow (00002). The primary purpose of this report is to record our current answers; hopefully those answers will turn out to be answers indeed. The group was formed in November 2010. In November 2010 Jim Gosler, Sandia Fellow, asked several of us several pointed questions about computer security metrics. Never mind that some of the best minds in the field have been trying to crack this nut without success for decades. Jim asked Campbell to lead an informal and unfunded group to answer the questions. With time Jim invited several more Sandians to join in. We met a number of times both with Jim and without him. At Jim's direction we contacted a number of people outside Sandia who Jim thought could help. For example, we interacted with IBM's T.J. Watson Research Center and held a one-day, videoconference workshop with them on the questions.

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TYPE SAND Report YEAR 2012
OSTIDOI
Results 51–75 of 144
Results 51–75 of 144