Related papers: Efficient Solution of Parameter Dependent Quasisep…
In this paper, we introduce a tensor neural network based machine learning method for solving the elliptic partial differential equations with random coefficients in a bounded physical domain. With the help of tensor product structure, we…
The Hadamard decomposition is a powerful technique for data analysis and matrix compression, which decomposes a given matrix into the element-wise product of two or more low-rank matrices. In this paper, we develop an efficient algorithm to…
Projection-based reduced order models are effective at approximating parameter-dependent differential equations that are parametrically separable. When parametric separability is not satisfied, which occurs in both linear and nonlinear…
The symmetric Nonnegative Matrix Factorization (NMF), a special but important class of the general NMF, has found numerous applications in data analysis such as various clustering tasks. Unfortunately, designing fast algorithms for the…
Several quantities important in condensed matter physics, quantum information, and quantum chemistry, as well as quantities required in meta-optimization of machine learning algorithms, can be expressed as gradients of implicitly defined…
Gradient-based optimization is a key ingredient of variational quantum algorithms, with applications ranging from quantum machine learning to quantum chemistry and simulation. The parameter-shift rule provides a hardware-friendly method for…
Distributed-memory matrix multiplication (MM) is a key element of algorithms in many domains (machine learning, quantum physics). Conventional algorithms for dense MM rely on regular/uniform data decomposition to ensure load balance. These…
The computational cost of many signal processing and machine learning techniques is often dominated by the cost of applying certain linear operators to high-dimensional vectors. This paper introduces an algorithm aimed at reducing the…
Constrained quasiconvex optimization problems appear in many fields, such as economics, engineering, and management science. In particular, fractional programming, which models ratio indicators such as the profit/cost ratio as fractional…
We propose a novel numerical approach to compute the Pareto front in multivariate polynomial multi-objective optimization problems. When the objective functions and (equality) constraints are multivariate polynomials, the Pareto front,…
In this study, an algorithm for computing the inverse of periodic k banded matrices, which are needed for solving the differential equations by using the finite differences, the solution of partial differential equations and the solution of…
Dynamical systems with quadratic or polynomial drift exhibit complex dynamics, yet compared to nonlinear systems in general form, are often easier to analyze, simulate, control, and learn. Results going back over a century have shown that…
We introduce two efficient algorithms for computing the partial Fourier transforms in one and two dimensions. Our study is motivated by the wave extrapolation procedure in reflection seismology. In both algorithms, the main idea is to…
We present a general class of machine learning algorithms called parametric matrix models. In contrast with most existing machine learning models that imitate the biology of neurons, parametric matrix models use matrix equations that…
In this paper we derive and analyze an algorithm for inverting quaternion matrices. The algorithm is an analogue of the Frobenius algorithm for the complex matrix inversion. On the theory side, we prove that our algorithm is more efficient…
The paper deals with the developing of the methodological backgrounds for the modeling and simulation of complex dynamical objects. Such backgrounds allow us to perform coordinate transformation and formulate the algorithm of its usage for…
We present algorithms for computing strongly singular and near-singular surface integrals over curved triangular patches, based on singularity subtraction, the continuation approach, and transplanted Gauss quadrature. We demonstrate the…
Author presents a study of certain category of the integrals, which might look quite difficult to compute, but in fact are easily computable, because they do not depend on the parameter in the integrand. As simple and elementary the…
A random matrix is likely to be well conditioned, and motivated by this well known property we employ random matrix multipliers to advance some fundamental matrix computations. This includes numerical stabilization of Gaussian elimination…
The pseudoinverse of a matrix, a generalized notion of the inverse, is of fundamental importance in linear algebra and, thereby, in many different fields. Despite its proven existence, an algorithmic approach is typically necessary to…