We develop spectral methods for ODEs and operator eigenvalue problems that are based on a least-squares formulation of the problem. The key tool is method rectangular generalized problems, which we extend to quasimatrices objects combining matrices. strength approach its flexibility lies in quasimatrix allowing basis functions be chosen arbitrarily, good choice (e.g., those obtained by solving ...

Community detection is a fundamental problem in network analysis with many methods available to estimate communities. Most of these assume that the number communities known, which often not case practice. We study simple and very fast method for estimating based on spectral properties certain graph operators, such as non-backtracking matrix Bethe Hessian matrix. show performs well under several...