Comment on “Lagrange-multiplier method in correlated-electron systems: Exact diagonalization study”

Comment on ‘‘Lagrange-multiplier method in correlated-electron systems: Exact diagonalization study’’

The Lagrange Multiplier Method for Dirichlet's Problem

The Lagrange multiplier method of Babuska for the approximate solution of Dirichlet's problem for second order elliptic equations is reformulated. Based on this formulation, new estimates for the error in the solution and the boundary flux are given. Efficient methods for the solution of the approximate problem are discussed.

Exact Diagonalization Study of Strongly Correlated Electron Models: Hole Pockets and Shadow Bands in the Doped T-j Model

A detailed exact-diagonalization study is made for the doping dependence of the single-particle spectral function A(k, ω) and momentum distribution function n(k) of the two-dimensional t−J model as a representative model for doped Mott insulators. The results for A(k, ω) show unambiguously that the rigid-band behavior is realized in the small-cluster t−J model: upon doping, the uppermost states...

The Augmented Lagrange Multiplier Method for Exact Recovery of Corrupted Low-Rank Matrices

This paper proposes scalable and fast algorithms for solving the Robust PCA problem, namely recovering a low-rank matrix with an unknown fraction of its entries being arbitrarily corrupted. This problem arises in many applications, such as image processing, web data ranking, and bioinformatic data analysis. It was recently shown that under surprisingly broad conditions, the Robust PCA problem c...

Comment on "Universal Fluctuations in Correlated Systems".

1 In [1], it is suggested that the probability distribution functions (PDF's) of fluctuating observables for critical systems in different universality classes exhibit a same form. This Comment concerns the PDF's for equilibrium systems. In [2], it is pointed out that the standard scaling form is a sufficient condition for the data collapse. The suggestion in [1] seems contradicting the idea of...