Based on the spectral divide-and-conquer algorithm by Nakatsukasa and Higham [SIAM J. Sci. Comput., 35(3):A1325–A1349, 2013], we propose a new algorithm for computing all the eigenvalues and eigenvectors of a symmetric banded matrix. For this purpose, we combine our previous work on the fast computation of spectral projectors in the so called HODLR format, with a novel technique for extracting ...

This paper is concerned with the cubic Szegő equation i∂tu = Π(|u|u), defined on the L Hardy space on the one-dimensional torus T, where Π : L(T)→ L+(T) is the Szegő projector onto the non-negative frequencies. For analytic initial data, it is shown that the solution remains spatial analytic for all time t ∈ (−∞,∞). In addition, we find a lower bound for the radius of analyticity of the solutio...

This paper explores the effectiveness of social network analysis and sentiment analysis in predicting trends. Our research focuses on predicting the success of new movies over their first four weeks in the box office after opening. Specifically, we try to predict prices on the Hollywood Stock Exchange (HSX), a prediction market on movie gross income, and predict the ratio of gross income to pro...

ôbjective: ône of non-confrontative methods for treatment of difficult issues such as grief is movie therapy which is an advanced form of bibliotherapy. the present study aimed at evaluating the effectiveness of group movie therapy (gmt) on reduction of intensity of grief experience in bereaved adolescent girls. methods: this was a quasi-experimental design with pretest-posttest and a follow up...