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As programmers turn to software-defined hardware (SDH) to maintain a high level of productivity while programming hardware to run complex algorithms, heavy-lifting must be done by the compiler to automatically partition on-chip arrays. In…

We study the tensor renormalization group (TRG) in the dimension larger than two as the Higher-order TRG (HOTRG) with the randomized SVD method. The randomized SVD and the detailed discussion on the low order tensor representation, we can…

Tensor network (TN) states, including entanglement renormalization (ER), can encompass a wider variety of entangled states. When the entanglement structure of the quantum state of interest is non-uniform in real space, accurately…

Using an autoencoder for dimensionality reduction, this paper presents a novel projection-based reduced-order model for eigenvalue problems. Reduced-order modelling relies on finding suitable basis functions which define a low-dimensional…

Singular value decomposition (SVD) is the mathematical basis of principal component analysis (PCA). Together, SVD and PCA are one of the most widely used mathematical formalism/decomposition in machine learning, data mining, pattern…

A new algorithm for eigenvalue problems for the fractional Jacobi type ODE is proposed. The algorithm is based on piecewise approximation of the coefficients of the differential equation with subsequent recursive procedure adapted from some…

Rank minimization can be converted into tractable surrogate problems, such as Nuclear Norm Minimization (NNM) and Weighted NNM (WNNM). The problems related to NNM, or WNNM, can be solved iteratively by applying a closed-form proximal…

The Schr\"odinger equation is at the heart of modern quantum mechanics. Since exact solutions of the ground state are typically intractable, standard approaches approximate Schr\"odinger equation as forms of nonlinear generalized eigenvalue…

This article introduces a tensor network subspace algorithm for the identification of specific polynomial state space models. The polynomial nonlinearity in the state space model is completely written in terms of a tensor network, thus…

In this paper, we develop a new reduced basis (RB) method, named as Single Eigenvalue Acceleration Method (SEAM), for second-order parabolic equations with homogeneous Dirichlet boundary conditions. The high-fidelity numerical method adopts…

Engineering simulations are usually based on complex, grid-based, or mesh-free methods for solving partial differential equations. The results of these methods cover large fields of physical quantities at very many discrete spatial…

Random projection (RP) is a classical technique for reducing storage and computational costs. We analyze RP-based approximations of convex programs, in which the original optimization problem is approximated by the solution of a…

The rising number of bridge collapses worldwide has compelled governments to introduce predictive maintenance strategies to extend structural lifespan. In this context, vibration-based Structural Health Monitoring (SHM) techniques utilizing…

The singular value decomposition (SVD) is commonly used in applications requiring a low rank matrix approximation. However, the singular vectors cannot be interpreted in terms of the original data. For applications requiring this type of…

Two widely used randomized algorithms are the sketch-and-solve method for least-squares regression and the randomized SVD for low-rank approximation. These algorithms apply a random embedding to compress a target matrix, and they perform…

VQE is currently one of the most widely used algorithms for optimizing problems using quantum computers. A necessary step in this algorithm is calculating the expectation value given a state, which is calculated by decomposing the…

Stochastic Gradient (SG) is the defacto iterative technique to solve stochastic optimization (SO) problems with a smooth (non-convex) objective $f$ and a stochastic first-order oracle. SG's attractiveness is due in part to its simplicity of…

Eigendecomposition (ED) is widely used in deep networks. However, the backpropagation of its results tends to be numerically unstable, whether using ED directly or approximating it with the Power Iteration method, particularly when dealing…

Randomized block Krylov subspace methods form a powerful class of algorithms for computing the extreme eigenvalues of a symmetric matrix or the extreme singular values of a general matrix. The purpose of this paper is to develop new…

In this paper, we propose a novel reduced-rank algorithm for direction of arrival (DOA) estimation based on the minimum variance (MV) power spectral evaluation. It is suitable to DOA estimation with large arrays and can be applied to…