Related papers: Evaluating a double integral using Euler's method …
Accurate evaluation of nearly singular integrals plays an important role in many boundary integral equation based numerical methods. In this paper, we propose a variant of singularity swapping method to accurately evaluate the layer…
The presence of second-order smoothness for objective functions of optimization problems can provide valuable information about their stability properties and help us design efficient numerical algorithms for solving these problems. Such…
This paper introduces a novel approach to approximating continuous functions over high-dimensional hypercubes by integrating matrix CUR decomposition with hyperinterpolation techniques. Traditional Fourier-based hyperinterpolation methods…
We present two new methods for multivariate exponential analysis. In [7], we developed a new algorithm for reconstruction of univariate exponential sums by exploiting the rational structure of their Fourier coefficients and reconstructing…
This paper deals with speeding up the convergence of a class of two-step iterative methods for solving linear systems of equations. To implement the acceleration technique, the residual norm associated with computed approximations for each…
A trajectory-following primal--dual interior-point method solves nonlinear optimization problems with inequality and equality constraints by approximately finding points satisfying perturbed Karush--Kuhn--Tucker optimality conditions for a…
Some numerical algorithms for elliptic eigenvalue problems are proposed, analyzed, and numerically tested. The methods combine advantages of the two-grid algorithm, two-space method, the shifted inverse power method, and the polynomial…
Renewed interest in mixed-precision algorithms has emerged due to growing data capacity and bandwidth concerns, as well as the advancement of GPUs, which enable significant speedup for low precision arithmetic. In light of this, we propose…
We present a numerical scheme that can be combined with any fixed boundary finite element based Poisson or Grad-Shafranov solver to compute the first and second partial derivatives of the solution to these equations with the same order of…
This paper studies the iteration-complexity of a new primal-dual algorithm based on Rockafellar's proximal method of multipliers (PMM) for solving smooth convex programming problems with inequality constraints. In each step, either a step…
We present a method for computing nearly singular integrals that occur when single or double layer surface integrals, for harmonic potentials or Stokes flow, are evaluated at points nearby. Such values could be needed in solving an integral…
The entropy of a binary symmetric Hidden Markov Process is calculated as an expansion in the noise parameter epsilon. We map the problem onto a one-dimensional Ising model in a large field of random signs and calculate the expansion…
Primal-dual splitting schemes are a class of powerful algorithms that solve complicated monotone inclusions and convex optimization problems that are built from many simpler pieces. They decompose problems that are built from sums, linear…
This study investigates the computational speed and accuracy of two numerical integration methods, cubature and sampling-based, for integrating an integrand over a 2D polygon. Using a group of rovers searching the Martian surface with a…
We propose implicit integrators for solving stiff differential equations on unit spheres. Our approach extends the standard backward Euler and Crank-Nicolson methods in Cartesian space by incorporating the geometric constraint inherent to…
We study a numerical approximation for a nonlinear variable-order fractional differential equation via an integral equation method. Due to the lack of the monotonicity of the discretization coefficients of the variable-order fractional…
We revisit the idea of numerically integrating the differential form of Feynman integrals. With a novel approach for the treatment of branch cuts, we develop an integrator capable of evaluating a basis of master integrals in double and…
Modern lunar-planetary ephemerides are numerically integrated on the observational timespan of more than 100 years (with the last 20 years having very precise astrometrical data). On such long timespans, not only finite difference…
We consider fractional isoperimetric problems of calculus of variations with double integrals via the recent modified Riemann-Liouville approach. A necessary optimality condition of Euler-Lagrange type, in the form of a multitime fractional…
A method is presented for the analytical evaluation of the singular and near-singular integrals arising in the Boundary Element Method solution of the Helmholtz equation. An error analysis is presented for the numerical evaluation of such…