Related papers: Evaluation of the matrix exponential function usin…
An algorithm for the evaluation of the complex exponential function is proposed which is quasi-linear in time and linear in space. This algorithm is based on a modified binary splitting method for the hypergeometric series and a modified…
Matrix completion aims to reconstruct a data matrix based on observations of a small number of its entries. Usually in matrix completion a single matrix is considered, which can be, for example, a rating matrix in recommendation system.…
Matrix factorization (MF) has been widely used to discover the low-rank structure and to predict the missing entries of data matrix. In many real-world learning systems, the data matrix can be very high-dimensional but sparse. This poses an…
Determination of linear combination of exponential functions with unknown rate constants from its sampled values is a problem of considerable interest. Here we present a constructive and explicit solution to this problem. Moments of such…
Purpose of writing this paper is to solve a transcendental function containing a product of a variable and its double exponential by a unique method of approximation. If the value of the said product is given, then its inverse function is…
Although persistent excitation is often acknowledged as a sufficient condition to exponentially converge in the field of adaptive parameter estimation, it must be noted that in practical applications this may be unguaranteed. Recently, more…
Computation of the large sparse matrix exponential has been an important topic in many fields, such as network and finite-element analysis. The existing scaling and squaring algorithm (SSA) is not suitable for the computation of the large…
In this paper, we propose an efficient exponential integrator finite element method for solving a class of semilinear parabolic equations in rectangular domains. The proposed method first performs the spatial discretization of the model…
Exact methods for exponentiation of matrices of dimension $N$ can be computationally expensive in terms of execution time ($N^{3}$) and memory requirements ($N^{2}$) not to mention numerical precision issues. A type of matrix often…
In this paper we extend the polynomial time integration framework to include exponential integration for both partitioned and unpartitioned initial value problems. We then demonstrate the utility of the exponential polynomial framework by…
The problem of iterated partial summations is solved for some discrete distributions defined on discrete supports. The power method, usually used as a computational approach to finding matrix eigenvalues and eigenvectors, is in some cases…
In our previous works, we proved that the inverse of the stiffness matrix of an $h$-version finite element method (FEM) applied to scalar second order elliptic boundary value problems can be approximated at an exponential rate in the block…
Modeling of physical systems includes extensive use of software packages that implement the accurate finite element method for solving differential equations considered along with the appropriate initial and boundary conditions. When the…
The exponential trapezoidal rule is proposed and analyzed for the numerical integration of semilinear integro-differential equations. Although the method is implicit, the numerical solution is easily obtained by standard fixed-point…
The natural exponential function is widely used in modeling many engineering and scientific systems. It is also an integral part of many neural network activation function such as sigmoid, tanh, ELU, RBF etc. Dedicated hardware accelerator…
We prove that the inverse of a positive-definite matrix can be approximated by a weighted-sum of a small number of matrix exponentials. Combining this with a previous result [OSV12], we establish an equivalence between matrix inversion and…
This paper introduces the exponential substitution calculus (ESC), a new presentation of cut elimination for IMELL, based on proof terms and building on the idea that exponentials can be seen as explicit substitutions. The idea in itself is…
We continue the study of truncated matrix-valued moment problems begun in arXiv:2310.00957. Let $q\in\mathbb{N}$. Suppose that $(\mathcal{X},\mathfrak{X})$ is a measurable space and $\mathcal{E}$ is a finite-dimensional vector space of…
A novel algorithm for computing the action of a matrix exponential over a vector is proposed. The algorithm is based on a multilevel Monte Carlo method, and the vector solution is computed probabilistically generating suitable random paths…
The time integration of semilinear parabolic problems by exponential methods of different kinds is considered. A new algorithm for the implementation of these methods is proposed. The algorithm evaluates the operators required by the…