相关论文: High-precision evaluation of Wigner's d-matrix by …
In this paper, a new ridge-type shrinkage estimator for the precision matrix has been proposed. The asymptotic optimal shrinkage coefficients and the theoretical loss were derived. Data-driven estimators for the shrinkage coefficients were…
A new uniform asymptotic approximation for the Wigner $6j$ symbol is given in terms of Wigner rotation matrices ($d$-matrices). The approximation is uniform in the sense that it applies for all values of the quantum numbers, even those near…
We calculate the `one-point function', meaning the marginal probability density function for any single eigenvalue, of real and complex Wishart correlation matrices. No explicit expression had been obtained for the real case so far. We…
By using determinantal representations of the W-weighted Drazin inverse previously obtained by the author within the framework of the theory of the column-row determinants, we get explicit formulas for determinantal representations of the…
An effective exact method is proposed for computing generalized eigenspaces of a matrix of integers or rational numbers. Keys of our approach are the use of minimal annihilating polynomials and the concept of the Jourdan-Krylov basis. A new…
Diagonalization, or eigenvalue decomposition, is very useful in many areas of applied mathematics, including signal processing and quantum physics. Matrix decomposition is also a useful tool for approximating matrices as the product of a…
We consider the characteristic function of linear spectral statistics of generalized Wigner matrices. We provide an expansion of the characteristic function with error $\mathcal{O} ( N^{-1})$ around its limiting Gaussian form, and identify…
Diagonalization of a large matrix is the computational bottleneck in many applications such as electronic structure calculations. We show that a speedup of over 30% can be achieved by exploiting 32-bit floating point operations, while…
We compute the $r$-matrix for the elliptic Euler-Calogero-Moser model. In the trigonometric limit we show that the model possesses an exact Yangian symmetry.
Over decades, the time evolution of Wigner functions along classical Hamiltonian flows has been used for approximating key signatures of molecular quantum systems. Such approximations are for example the Wigner phase space method, the…
In this paper, we first establish an evaluation formula to calculate Wiener integrals of functionals on Wiener space. We then apply our evaluation formula to carry out very easily calculating for the analytic Fourier-Feynman transform of…
We present a general class of compressed sensing matrices which are then demonstrated to have associated sublinear-time sparse approximation algorithms. We then develop methods for constructing specialized matrices from this class which are…
An efficient method is proposed for computing the structure of Jordan blocks of a matrix of integers or rational numbers by exact computation. We have given a method for computing Jordan chains of a matrix with exact computation. However,…
In this paper we review the theory of the Yang-Baxter equation related to the 6-vertex model and its higher spin generalizations. We employ a 3D approach to the problem. Starting with the 3D R-matrix, we consider a two-layer projection of…
The Strassen algorithm and Winograd's variant accelerate matrix multiplication by using fewer arithmetic operations than standard matrix multiplication. Although many papers have been published to accelerate single- as well as…
We construct general Wigner rotations for both massive and massless particles in $D$-dimensional spacetime. We work out the explicit expressions of these Wigner rotations for arbitrary Lorentz transformations. We study the relation between…
To evaluate ESR spectrum at finite temperatures for specified spatial configurations of spins is very important issue to study quantum spin systems. Although a direct numerical estimation of the Kubo formula provides exact data, the…
The efficient computer optimization of magnetic resonance pulses and pulse sequences involves the calculation of a problem-adapted cost function as well as its gradients with respect to all controls applied. The gradients generally can be…
We describe a variational approach to solving Anderson impurity models by means of exact diagonalization. Optimized parameters of a discretized auxiliary model are obtained on the basis of the Peierls-Feynman-Bogoliubov principle. Thereby,…
The goal of this article is that of understanding how the oscillation and concentration effects developed by a sequence of functions in $\mathbb{R}^{d} $ are modified by the action of Sampling and Reconstruction operators on regular grids.…