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This paper is devoted to proposing a general weighted low-rank recovery model and designing a fast SVD-free computational scheme to solve it. First, our generic weighted low-rank recovery model unifies several existing approaches in the…
In this paper, we first discuss the optimal convergence of the adaptive finite element methods for non-self-adjoint eigenvalue problems. We present new theoretical error estimators and computable error estimators for multiple and clustered…
We present a comparative study of the application of modern eigenvalue algorithms to an eigenvalue problem arising in quantum physics, namely, the computation of a few interior eigenvalues and their associated eigenvectors for the large,…
In this paper a quaternion approach of enhancement method is proposed in which color in the image is considered as a single entity. This new method is referred as the alpha-rooting method of color image enhancement by the two-dimensional…
In this paper, we first establish the convergence criteria of the residual iteration method for solving quadratic eigenvalue problem- s. We analyze the impact of shift point and the subspace expansion on the convergence of this method. In…
Deep probabilistic generative models have achieved incredible success in many fields of application. Among such models, variational autoencoders (VAEs) have proved their ability in modeling a generative process by learning a latent…
By exploiting the invariance of the molecular Hamiltonian by a unitary transformation of the orbitals it is possible to significantly shorter the depth of the variational circuit in the Variational Quantum Eigensolver (VQE) algorithm by…
Portfolio optimization is a fundamental problem in finance that aims to determine the optimal allocation of assets within a portfolio to maximize returns while minimizing risk. It can be formulated as a Quadratic Unconstrained Binary…
Versions of GMRES with deflation of eigenvalues are applied to lattice QCD problems. Approximate eigenvectors corresponding to the smallest eigenvalues are generated at the same time that linear equations are solved. The eigenvectors…
We propose a new type of multilevel method for solving eigenvalue problems based on Newton iteration. With the proposed iteration method, solving eigenvalue problem on the finest finite element space is replaced by solving a small scale…
Quantum computing holds immense promise for simulating quantum systems, a critical task for advancing our understanding of complex quantum phenomena. One of the primary goals in this domain is to accurately approximate the ground state of…
The thesis deals with Quantum Algorithms for solving Hard Constrained Optimization Problems. It shows how quantum computers can solve difficult everyday problems such as finding the best schedule for social workers or the path of a robot…
Broyden's method is a general method commonly used for nonlinear systems of equations, when very little information is available about the problem. We develop an approach based on Broyden's method for nonlinear eigenvalue problems. Our…
The accurate computation of ground and excited states of many-fermion quantum systems is one of the most consequential, contemporary challenges in the physical and computational sciences whose solution stands to benefit significantly from…
Many fields of science and engineering require finding eigenvalues and eigenvectors of large matrices. The solutions can represent oscillatory modes of a bridge, a violin, the disposition of electrons around an atom or molecule, the…
We describe a quantum algorithm for finding the smallest eigenvalue of a Hermitian matrix. This algorithm combines Quantum Phase Estimation and Quantum Amplitude Estimation to achieve a quadratic speedup with respect to the best classical…
Edge networks call for communication efficient (low overhead) and robust distributed optimization (DO) algorithms. These are, in fact, desirable qualities for DO frameworks, such as federated edge learning techniques, in the presence of…
Quantum algorithms for estimating the eigenvalues of matrices, including the phase estimation algorithm, serve as core subroutines in a wide range of quantum algorithms, including those in quantum chemistry and quantum machine learning. The…
The next-next-to-leading order QCD corrections to the e+e- annihilation into hadrons are considered. The stability of the predictions with respect to change of the renormalization scheme is discussed in detail for the case of five, four and…
The convection-diffusion eigenvalue problems are hot topics, and computational mathematics community and physics community are concerned about them in recent years. In this paper, we consider the a posteriori error analysis and the adaptive…