We present a density fitted local configuration interaction singles (CIS) method for calculating optical band gaps in 1D-periodic systems. The method is based on the Davidson diagonalization procedure, carried out in the reciprocal space. The one-electron part of the matrix-vector products is also evaluated in the reciprocal space, where the diagonality of the Fock matrix can be exploited. The ...

We derive closed formulas for the condition number of a linear function of the total least squares solution. Given an over determined linear system Ax = b, we show that this condition number can be computed using the singular values and the right singular vectors of [A, b] and A. We also provide an upper bound that requires the computation of the largest and the smallest singular value of [A, b...

Suppose that T is a stochastic matrix. We propose an algorithm for identifying clusters in the Markov chain associated with T. The recursive nature, and order to identify clusters, it uses sign pattern of left singular vector second smallest value Laplacian matrix I−T. prove number results justify algorithm's approach, illustrate performance several numerical examples.

In multi-class support vector machine (MSVM) for classification, one core issue is to regularize the coefficient vectors to reduce overfitting. Various regularizers have been proposed such as `2, `1, and trace norm. In this paper, we introduce a new type of regularization approach – angular regularization, that encourages the coefficient vectors to have larger angles such that class regions can...