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A class of algorithms for the solution of discrete material optimization problems in electromagnetic applications is discussed. The idea behind the algorithm is similar to that of the sequential programming. However, in each major iteration…
We present a highly efficient molecular dynamics scheme for calculating the concentration depth profile of dopants in ion irradiated materials. The scheme incorporates several methods for reducing the computational overhead, plus a rare…
The extension of the highly-optimized local natural orbital (LNO) CCSD(T) method is presented for high-spin open-shell molecules. The techniques enabling the outstanding efficiency of the closed-shell LNO-CCSD(T) variant are adopted,…
We have used diffusion quantum Monte Carlo (DMC) calculations to study the pressure-induced phase transition from the diamond to $\beta$-tin structure in silicon. The calculations employ the pseudopotential technique and systematically…
Robust tensor CP decomposition involves decomposing a tensor into low rank and sparse components. We propose a novel non-convex iterative algorithm with guaranteed recovery. It alternates between low-rank CP decomposition through gradient…
We propose the variational quantum singular value decomposition based on encoding the elements of the considered { $N\times N$} matrix into the state of a quantum system of appropriate dimension. This method doesn't use the expansion of…
We present a novel framework for Linear Combination of Unitaries (LCU)-style decomposition tailored to structured sparse matrices, which frequently arise in the numerical solution of partial differential equations (PDEs). While LCU is a…
This paper proposes two compressive sampling based time of arrival (TOA) estimation algorithms using a sub-Nyquist rate receiver. We also describe a novel compressive sampling dictionary design for the compact representation of the received…
We provide microscopic diagrammatic derivations of the Molecular Coherent Potential Approximation (MCA) and Dynamical Cluster Approximation (DCA) and show that both are Phi-derivable. The MCA (DCA) maps the lattice onto a self-consistently…
The classic method for computing the spectral decomposition of a real symmetric matrix, the Jacobi algorithm, can be accelerated by using mixed precision arithmetic. The Jacobi algorithm is aiming to reduce the off-diagonal entries…
The robust principal component analysis (RPCA) decomposes a data matrix into a low-rank part and a sparse part. There are mainly two types of algorithms for RPCA. The first type of algorithm applies regularization terms on the singular…
In this work, we extend the fractional linear multistep methods in [C. Lubich, SIAM J. Math. Anal., 17 (1986), pp.704--719] to the tempered fractional integral and derivative operators in the sense that the tempered fractional derivative…
A recently developed density functional method, within Hohenberg-Kohn-Sham framework, is used for faithful description of atoms, molecules in Cartesian coordinate grid, by using an LCAO-MO ansatz. Classical Coulomb potential is obtained by…
Machine learning interatomic potentials (MLIPs) are routinely used atomic simulations, but generating databases of atomic configurations used in fitting these models is a laborious process, requiring significant computational and human…
Principal component analysis (PCA) requires the computation of a low-rank approximation to a matrix containing the data being analyzed. In many applications of PCA, the best possible accuracy of any rank-deficient approximation is at most a…
Currently, existing tensor recovery methods fail to recognize the impact of tensor scale variations on their structural characteristics. Furthermore, existing studies face prohibitive computational costs when dealing with large-scale…
We describe a Lanczos-based algorithm for approximating the product of a rational matrix function with a vector. This algorithm, which we call the Lanczos method for optimal rational matrix function approximation (Lanczos-OR), returns the…
The GW approach produces highly accurate quasiparticle energies, but its application to large systems is computationally challenging, which can be largely attributed to the difficulty in computing the inverse dielectric matrix. To address…
The Bregman-Kaczmarz method is an iterative method which can solve strongly convex problems with linear constraints and uses only one or a selected number of rows of the system matrix in each iteration, thereby making it amenable for…
Variational formulations of reconstruction in computed tomography have the notable drawback of requiring repeated evaluations of both the forward Radon transform and either its adjoint or an approximate inverse transform which are…