Convergence of restarted Krylov subspaces to invariant subspaces

The performance of Krylov subspace eigenvalue algorithms for large matrices can be measured by the angle between a desired invariant subspace and the Krylov subspace. We develop general bounds for this convergence that include the effects of polynomial restarting and impose no restrictions concerning the diagonalizability of the matrix or its degree of non-normality. Associated with a desired set of eigenvalues is a maximum ``reachable invariant subspace'' that can be developed from the given starting vector. Convergence for this distinguished subspace is bounded in terms involving a polynomial approximation problem. Elementary results from potential theory lead to convergence rate estimates and suggest restarting strategies based on optimal approximation points (e.g., Leja or Chebyshev points); exact shifts are evaluated within this framework. Computational examples illustrate the utility of these results. Origins of superlinear effects are also described

Community Analysis Report No. 1: Dealing with Japanese-Americans, Oct 1942

https://scholarlycommons.pacific.edu/cook-nisei/1118/thumbnail.jp

Community Analysis Report No. 1: Dealing with Japanese-Americans, Oct 1942

https://scholarlycommons.pacific.edu/cook-nisei/1118/thumbnail.jp

Further Evidence that Exclusive Breast-Feeding Reduces Mother-to-Child HIV Transmission Compared With Mixed Feeding

The author discusses the results of the Zambia Exclusive Breastfeeding Study, recently published inPLoS ONE

Perspective: Advancing the science regarding temporomandibular disorders

This Special Issue was initiated in response to the call for improved research by the National Academies of Sciences, Engineering, and Medicine (NASEM) (United States) Consensus Study Report on Temporomandibular Disorders (TMDs), a set of putatively localized musculoskeletal conditions. In this Special Issue, the importance of systems biology for TMDs emerges from each of three separate publications. The importance of systems biology to patients is anchored in two domains—laboratory research and clinical observation. The three publications fully speak to the underlying goals in the NASEM recommendations for initiatives: that research on TMDs needs to broaden, that integration between basic and clinical science needs to improve, and that while better evidence is needed, clinicians need to utilize the evidence that already exists. All three of these initiatives, taken together, would lead to better understanding of these complex diseases and to better care of patients with these diseases

Dealing with Japanese Americans.

Community Analysis Report No. 1. October 1942