Related papers: Lowest eigenvalue of the nuclear shell model Hamil…
We establish new bounds on the minimum number of distinct eigenvalues among real symmetric matrices with nonzero off-diagonal pattern described by the edges of a graph and apply these to determine the minimum number of distinct eigenvalues…
The widely used nuclear norm heuristic for rank minimization problems introduces a regularization parameter which is difficult to tune. We have recently proposed a method to approximate the regularization path, i.e., the optimal solution as…
The notions of weak and strong minimizability of a matrix intertwining operator are introduced. Criterion of strong minimizability of a matrix intertwining operator is revealed. Criterion and sufficient condition of existence of a constant…
A method based on the envelope theory is presented to compute approximate solutions for $N$-body Hamiltonians with identical particles in $D$ dimensions ($D\ge 2$). In some favorable cases, the approximate eigenvalues can be analytically…
A novel method for performing model updating on finite element models is presented. The approach is particularly tailored to modal analyses of buildings, by which the lowest frequencies, obtained by using sensors and system identification…
In the first part of the present work the $\mu-\tau $ symmetry of the neutrino mass matrix is perturbed at its minimal level in order to produce deviation from Tri-bimaximal mixing (TBM), which includes nonzero value of reactor angle…
We propose a procedure to determine the effective nuclear shell-model Hamiltonian in a truncated space from a self-consistent mean-field model, e.g., the Skyrme model. The parameters of pairing plus quadrupole-quadrupole interaction with…
The computation of eigenvalues of large-scale matrices arising from finite element discretizations has gained significant interest in the last decade. Here we present a new algorithm based on slicing the spectrum that takes advantage of the…
Originally developed for imputing missing entries in low rank, or approximately low rank matrices, matrix completion has proven widely effective in many problems where there is no reason to assume low-dimensional linear structure in the…
A powerful method for calculating the eigenvalues of a Hamiltonian operator consists of converting the energy eigenvalue equation into a matrix equation by means of an appropriate basis set of functions. The convergence of the method can be…
First self-consistent realistic shell-model calculation for the light p-shell nuclei is performed, starting from the high-precision nucleon-nucleon (NN) CD-Bonn potential. This realistic potential is renormalized deriving a low-momentum NN…
Nonlinear least-squares problems are a special class of unconstrained optimization problems in which their gradient and Hessian have special structures. In this paper, we exploit these structures and proposed a matrix-free algorithm with a…
Random matrix theory allows one to deduce the eigenvalue spectrum of a large matrix given only statistical information about its elements. Such results provide insight into what factors contribute to the stability of complex dynamical…
We present a method to discretize the Kohn-Sham Hamiltonian matrix in the pseudopotential framework by a small set of basis functions automatically contracted from a uniform basis set such as planewaves. Each basis function is localized…
Positive semi-definite matrices commonly occur as normal matrices of least squares problems in statistics or as kernel matrices in machine learning and approximation theory. They are typically large and dense. Thus algorithms to solve…
This work is concerned with approximating the smallest eigenvalue of a parameter-dependent Hermitian matrix $A(\mu)$ for many parameter values $\mu \in \mathbb{R}^P$. The design of reliable and efficient algorithms for addressing this task…
Given a structured matrix $A$ we study the problem of finding the closest normal matrix with the same structure. The structures of our interest are: Hamiltonian, skew-Hamiltonian, per-Hermitian, and perskew-Hermitian. We develop a…
We study low-rank matrix regression in settings where matrix-valued predictors and scalar responses are observed across multiple individuals. Rather than assuming a fully homogeneous coefficient matrices across individuals, we accommodate…
A means to take advantage of molecular similarity to lower the computational cost of electronic structure theory is explored, in which parameters are embedded into a low-cost, low-level (LL) ab initio model and adjusted to obtain agreement…
We construct explicit formulae for the eigenvalues of certain invariants of the Lie superalgebra gl(m|n) using characteristic identities. We discuss how such eigenvalues are related to reduced Wigner coefficients and the reduced matrix…