Leading Practices: Agency Acquisition Policies Could Better Implement Key Product Development Principles

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Person to Person in China

While still in the midst of their study abroad experiences, students at Linfield College write reflective essays. Their essays address issues of cultural similarity and difference, compare lifestyles, mores, norms, and habits between their host countries and home, and examine changes in perceptions about their host countries and the United States. In this essay, Erin Carson describes her observations during her study abroad program at Peking University in Beijing, China

Single-pass Nystr\"{o}m approximation in mixed precision

Low rank matrix approximations appear in a number of scientific computing applications. We consider the Nystr\"{o}m method for approximating a positive semidefinite matrix $A$. The computational cost of its single-pass version can be decreased by running it in mixed precision, where the expensive products with $A$ are computed in a precision lower than the working precision. We bound the extra finite precision error which is compared to the error of the Nystr\"{o}m approximation in exact arithmetic and develop a heuristic to identify when the approximation quality is not affected by the low precision computation. Further, the mixed precision Nystr\"{o}m method can be used to inexpensively construct a limited memory preconditioner for the conjugate gradient method. We bound the condition number of the resulting preconditioned coefficient matrix, and experimentally show that such a preconditioner can be effective

Mixed Precision Rayleigh Quotient Iteration for Total Least Squares Problems

With the recent emergence of mixed precision hardware, there has been a renewed interest in its use for solving numerical linear algebra problems fast and accurately. The solution of total least squares problems, i.e., solving $\min_{E,f} \| [E, f]\|_F$ subject to $(A+E)x=b+f$, arises in numerous application areas. The solution of this problem requires finding the smallest singular value and corresponding right singular vector of $[A,b]$, which is challenging when $A$ is large and sparse. An efficient algorithm for this case due to Bj\"{o}rck et al., called RQI-PCGTLS, is based on Rayleigh quotient iteration coupled with the conjugate gradient method preconditioned via Cholesky factors. We develop a mixed precision variant of this algorithm, called RQI-PCGTLS-MP, in which up to three different precisions can be used. We assume that the lowest precision is used in the computation of the preconditioner, and give theoretical constraints on how this precision must be chosen to ensure stability. In contrast to the standard least squares case, for total least squares problems, the constraint on this precision depends not only on the matrix $A$, but also on the right-hand side $b$. We perform a number of numerical experiments on model total least squares problems used in the literature, which demonstrate that our algorithm can attain the same accuracy as RQI-PCGTLS albeit with a potential convergence delay due to the use of low precision. Performance modeling shows that the mixed precision approach can achieve up to a $4\times$ speedup depending on the size of the matrix and the number of Rayleigh quotient iterations performed.Comment: 20 page

Blogging as a Medium of Social Support During the Adoption Process: A Phenomenological Study of Adopting Parent-Bloggers.

The purpose of this research was to investigate the community of support prospective adoptive parents create by way of blogging during the adoption process. This study used phenomenology and grounded theory strategies as they pertain to the qualitative method inquiry to collect data through in depth interviews of nine participants, field notes, blog reading and relating artifacts. In order to get a balanced view of the phenomenon, this study included both blogger and non-blogger adoptive parents, who all participated in subsequent open-ended interviews. To analyze data, I used the following analytical tools: servant leadership, narrative paradigm, social support, and care theories. Completion of this research created greater understanding of how social media invites interactions and connections that may not happen otherwise between people who shared the common purpose to adopt. Findings of this study revealed the following: blogging built a support community for adoptive parents; it offered a place to share information and process emotions; it became a medium for adoptive parents to tell their stories; in particular, writing blogs turned blogging parents into servant leaders whose experience pave the way for future generations. These findings suggest that future prospective adoptive parents could use blogs to research sources and to find support groups both online and otherwise whose help could guide them down the least stressful path of adopting a child

Mixed Precision Iterative Refinement with Adaptive Precision Sparse Approximate Inverse Preconditioning

Hardware trends have motivated the development of mixed precision algo-rithms in numerical linear algebra, which aim to decrease runtime while maintaining acceptable accuracy. One recent development is the development of an adaptive precision sparse matrix-vector produce routine, which may be used to accelerate the solution of sparse linear systems by iterative methods. This approach is also applicable to the application of inexact preconditioners, such as sparse approximate inverse preconditioners used in Krylov subspace methods. In this work, we develop an adaptive precision sparse approximate inverse preconditioner and demonstrate its use within a five-precision GMRES-based iterative refinement method. We call this algorithm variant BSPAI-GMRES-IR. We then analyze the conditions for the convergence of BSPAI-GMRES-IR, and determine settings under which BSPAI-GMRES-IR will produce similar backward and forward errors as the existing SPAI-GMRES-IR method, the latter of which does not use adaptive precision in preconditioning. Our numerical experiments show that this approach can potentially lead to a reduction in the cost of storing and applying sparse approximate inverse preconditioners, although a significant reduction in cost may comes at the expense of increasing the number of GMRES iterations required for convergence

Mixed precision GMRES-based iterative refinement with recycling

summary:With the emergence of mixed precision hardware, mixed precision GMRES-based iterative refinement schemes for solving linear systems $Ax=b$ have recently been developed. However, in certain settings, GMRES may require too many iterations per refinement step, making it potentially more expensive than the alternative of recomputing the LU factors in a higher precision. In this work, we incorporate the idea of Krylov subspace recycling, a well-known technique for reusing information across sequential invocations, of a Krylov subspace method into a mixed precision GMRES-based iterative refinement solver. The insight is that in each refinement step, we call preconditioned GMRES on a linear system with the same coefficient matrix $A$. In this way, the GMRES solves in subsequent refinement steps can be accelerated by recycling information obtained from previous steps. We perform numerical experiments on various random dense problems, Toeplitz problems, and problems from real applications, which confirm the benefits of the recycling approach

70 years of Krylov subspace methods: The journey continues

Using computed examples for the Conjugate Gradient method and GMRES, we recall important building blocks in the understanding of Krylov subspace methods over the last 70 years. Each example consists of a description of the setup and the numerical observations, followed by an explanation of the observed phenomena, where we keep technical details as small as possible. Our goal is to show the mathematical beauty and hidden intricacies of the methods, and to point out some persistent misunderstandings as well as important open problems. We hope that this work initiates further investigations of Krylov subspace methods, which are efficient computational tools and exciting mathematical objects that are far from being fully understood.Comment: 38 page