David Fong

David Fong, Michael Saunders

An iterative method LSMR is presented for solving linear systems $Ax=b$ and least-squares problem $\min \norm{Ax-b}_2$, with $A$ being sparse or a fast linear operator. LSMR is based on the Golub-Kahan bidiagonalization process. It is analytically equivalent to the MINRES method applied to the normal equation $A\T Ax = A\T b$, so that the quantities $\norm{A\T r_k}$ are monotonically decreasing (where $r_k = b - Ax_k$ is the residual for the current iterate $x_k$). In practice we observe that $\norm{r_k}$ also decreases monotonically. Compared to LSQR, for which only $\norm{r_k}$ is monotonic, it is safer to terminate LSMR early. Improvements for the new iterative method in the presence of extra available memory are also explored.

David Fong, Tianshu Chu, Matthew Heflin et al.

We introduce a multi-layer perceptron (MLP) called the COVID-19 Depression and Anxiety Predictor (CoDAP) to predict mental health trends, particularly anxiety and depression, during the COVID-19 pandemic. Our method utilizes a comprehensive dataset, which tracked mental health symptoms weekly over ten weeks during the initial COVID-19 wave (April to June 2020) in a diverse cohort of U.S. adults. This period, characterized by a surge in mental health symptoms and conditions, offers a critical context for our analysis. Our focus was to extract and analyze patterns of anxiety and depression through a unique lens of qualitative individual attributes using CoDAP. This model not only predicts patterns of anxiety and depression during the pandemic but also unveils key insights into the interplay of demographic factors, behavioral changes, and social determinants of mental health. These findings contribute to a more nuanced understanding of the complexity of mental health issues in times of global health crises, potentially guiding future early interventions.