In this article, we propose a computationally efficient approach to estimate (large) p-dimensional covariance matrices of ordered (or longitudinal) data based on an independent sample of size n. To do this, we construct the estimator based on a k-band partial autocorrelation matrix with the number of bands chosen using an exact multiple hypothesis testing procedure. This approach is considerabl...

in this paper energy bands and berry curvature of graphene was studied. desired hamiltonian regarding the next-nearest neighbors obtained by tight binding model. by using the second quantization approach, the transformation matrix is calculated and the hamiltonian of system is diagonalized. with this hamiltonian, the band structure and wave function can be calculated. by using calculated wave f...

We construct a class of matrix-valued Schrödinger operators with prescribed finite-band spectra of maximum spectral multiplicity. The corresponding matrix potentials are shown to be stationary solutions of the KdV hierarchy. The methods employed in this paper rely on matrix-valued Herglotz functions, Weyl–Titchmarsh theory, pencils of matrices, and basic inverse spectral theory for matrix-value...

In this paper we will derive a solver for a symmetric strongly nonsingular higher order generator representable semiseparable plus band matrix. The solver we will derive is based on the Levinson algorithm, which is used for solving strongly nonsingular Toeplitz systems. In a first part an O(p 2 n) solver for a semiseparable matrix of semiseparability rank p is derived, and in a second part we d...

We study spectra and pseudospectra of certain bounded linear operators on l(Z) . The operators are generally non-normal, and their matrix representation has a characteristic offdiagonal decay. Based on a result of Chandler-Wilde, Chonchaiya and Lindner for tridiagonal infinite matrices, we demonstrate an efficient algorithm for the computation of upper and lower bounds on the pseudospectrum of ...

The four existing stable factorization methods for symmetric indefinite pivoting (row or column exchanges) maintains a band structure in the reduced matrix and the factors, but destroys symmetry completely once an off-diagonal pivot is used. Two-by-two block pivoting maintains symmetry at all times, but quickly destroys the band structure. Gaussian reduction to tridiagonal also maintains symmet...

the optical spectrum band positions and epr parameters (g factors g//, g^ and hyperfine structure constants a// and a^) for vo2+ ions in zn(antipyrine)2(no3)2 are theoretically studied from the complete diagonalization (of energy matrix) method (cdm) and the perturbation theory method (ptm). in the two methods, the contributions from the spin–orbit (so) coupling of central 3dn ion and ligand ar...

Yasuhiro Hayashi, Nozomu Okino, Yoshimitsu Kakuta, Toshihide Shikanai , Motohiro Tani**, Hisashi Narimatsu, and Makoto Ito From the Department of Bioscience and Biotechnology, Graduate School of Bioresource and Bioenvironmental Sciences, and **Department of Chemistry, Faculty of Science, Kyushu University, 6-10-1 Hakozaki, Higashi-ku, Fukuoka 812-8581, Japan, the Research Center for Medical Gly...