Related papers: Improved power methods for computing eigenvalues o…
In this paper, we extend the Chen and Moore determinants of quaternion Hermitian} matrices to dual quaternion Hermitian matrices. We show the Chen determinant of dual quaternion Hermitian {matrices is invariant under addition, switching,…
The electron pair approximation offers a resource efficient variational quantum eigensolver (VQE) approach for quantum chemistry simulations on quantum computers. With the number of entangling gates scaling quadratically with system size…
Electronic structure calculation of atoms and molecules, in the past few decades has largely been dominated by density functional methods. This is primarily due to the fact that this can account for electron correlation effects in a…
We present a novel technique for sparse principal component analysis. This method, named Eigenvectors from Eigenvalues Sparse Principal Component Analysis (EESPCA), is based on the formula for computing squared eigenvector loadings of a…
This paper considers decentralized consensus optimization problems where nodes of a network have access to different summands of a global objective function. Nodes cooperate to minimize the global objective by exchanging information with…
We explore the block nature of the matrix representation of multiplex networks, introducing a new formalism to deal with its spectral properties as a function of the inter-layer coupling parameter. This approach allows us to derive…
We employ the M-P inverses and ranks of quaternion matrices to establish the necessary and sufficient conditions for solving a system of the dual quaternion matrix equations $(AX, XC) = (B, D)$, along with providing an expression for its…
Dual complex numbers can represent rigid body motion in 2D spaces. Dual complex matrices are linked with screw theory, and have potential applications in various areas. In this paper, we study low rank approximation of dual complex…
The paper describes several efficient parallel implementations of the one-sided hyperbolic Jacobi-type algorithm for computing eigenvalues and eigenvectors of Hermitian matrices. By appropriate blocking of the algorithms an almost ideal…
Recently a method for adiabatic quantum computation has been proposed and there has been considerable speculation about its efficiency for NP-complete problems. Heuristic arguments in its favor are based on the unproven assumption of an…
We present a new algorithm for solving an eigenvalue problem for a real symmetric matrix which is a rank-one modification of a diagonal matrix. The algorithm computes each eigenvalue and all components of the corresponding eigenvector with…
We present a new transform, triple dqds, to help to compute the eigenvalues of a real tridiagonal matrix C using real arithmetic. The algorithm uses the real dqds transform to shift by a real number and triple dqds to shift by a complex…
We present a symbolic decomposition of the Pearson chi-square statistic with unequal cell probabilities, by presenting Hadamard-type matrices whose columns are eigenvectors of the variance-covariance matrix of the cell counts. All of the…
A previously developed quantum reduced-order model is revised and applied, together with the domain decomposition, to develop the quantum element method (QEM), a methodology for fast and accurate simulation of quantum eigenvalue problems.…
Eigensystem Realization Algorithm (ERA) is a data-driven approach for subspace system identification and is widely used in many areas of engineering. However, the computational cost of the ERA is dominated by a step that involves the…
A simple and efficient variational method is introduced to accelerate the convergence of the eigenenergy computations for a Hamiltonian H with singular potentials. Closed-form analytic expressions in N dimensions are obtained for the matrix…
This paper points out that the differential quadrature (DQ) and differential cubature (DC) methods due to their global domain property are more efficient for nonlinear problems than the traditional numerical techniques such as finite…
Quaternions are important for a wide variety of rotation-related problems in computer graphics, machine vision, and robotics. We study the nontrivial geometry of the relationship between quaternions and rotation matrices by exploiting the…
This paper considers the sparse eigenvalue problem, which is to extract dominant (largest) sparse eigenvectors with at most $k$ non-zero components. We propose a simple yet effective solution called truncated power method that can…
Such problems as computation of spectra of spin chains and vibrational spectra of molecules can be written as high-dimensional eigenvalue problems, i.e., when the eigenvector can be naturally represented as a multidimensional tensor. Tensor…