Efficient Algorithms for Solving Structured Eigenvalue Problems Arising in the Description of Electronic Excitations

Matrices arising in linear-response time-dependent density functional theory and many-body perturbation theory, in particular in the Bethe-Salpeter approach, show a 2 × 2 block structure. The motivation to devise new algorithms, instead of using general purpose eigenvalue solvers, comes from the need to solve large problems on high performance computers. This requires parallelizable and communication-avoiding algorithms and implementations. We point out various novel directions for diagonalizing structured matrices. These include the solution of skew-symmetric eigenvalue problems in ELPA, as well as structure preserving spectral divide-and-conquer schemes employing generalized polar decompostions

A Structure-Preserving Divide-and-Conquer Method for Pseudosymmetric Matrices

We devise a spectral divide-and-conquer scheme for matrices that are self-adjoint with respect to a given indefinite scalar product (i.e. pseudosymmetic matrices). The pseudosymmetric structure of the matrix is preserved in the spectral division, such that the method can be applied recursively to achieve full diagonalization. The method is well-suited for structured matrices that come up in computational quantum physics and chemistry. In this application context, additional definiteness properties guarantee a convergence of the matrix sign function iteration within two steps when Zolotarev functions are used. The steps are easily parallelizable. Furthermore, it is shown that the matrix decouples into symmetric definite eigenvalue problems after just one step of spectral division

Routinely randomize potential sources of measurement reactivity to estimate and adjust for biases in subjective reports

With the advent of online and app-based studies, researchers in psychology are making increasing use of repeated subjective reports. The new methods open up opportunities to study behavior in the field and to map causal processes, but they also pose new challenges. Recent work has added initial elevation bias to the list of common pitfalls; here, higher negative states (i.e., thoughts and feelings) are reported on the first day of assessment than on later days. This article showcases a new approach to addressing this and other measurement reactivity biases. Specifically, we employed a planned missingness design in a daily diary study of more than 1,300 individuals who were assessed over a period of up to 70 days to estimate and adjust for measurement reactivity biases. We found that day of first item presentation, item order, and item number were associated with only negligible bias: Items were not answered differently depending on when and where they were shown. Initial elevation bias may thus be more limited than has previously been reported or it may act only at the level of the survey, not at the item level. We encourage researchers to make design choices that will allow them to routinely assess measurement reactivity biases in their studies. Specifically, we advocate the routine randomization of item display and order, as well as of the timing and frequency of measurement. Randomized planned missingness makes it possible to empirically gauge how fatigue, familiarity, and learning interact to bias responses