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The problem of minimizing a continuously differentiable convex function over an intersection of closed convex sets is ubiquitous in applied mathematics. It is particularly interesting when it is easy to project onto each separate set, but…

This paper presents a new uniquely solvable boundary integral equation for computing the conformal mapping, its derivative and its inverse from bounded multiply connected regions onto the five classical canonical slit regions. The integral…

A method for the multifidelity Monte Carlo (MFMC) estimation of statistical quantities is proposed which is applicable to computational budgets of any size. Based on a sequence of optimization problems each with a globally minimizing…

Newton method is one of the most powerful methods for finding solutions of nonlinear equations and for proving their existence. In its "pure" form it has fast convergence near the solution, but small convergence domain. On the other hand…

We present approximate analytical solutions to the Hamiltonian and momentum constraint equations, corresponding to systems composed of two black holes with arbitrary linear and angular momentum. The analytical nature of these initial data…

The present work provides a critical assessment of numerical solutions of the space-fractional diffusion-advection equation, which is of high significance for applications in various natural sciences. In view of the fact that, in contrast…

We consider the product of a compact Riemannian manifold without boundary and null scalar curvature with a compact Riemannian manifold with boundary, null scalar curvature and constant mean curvature on the boundary. We use bifurcation…

The numerical solution of an ordinary differential equation can be interpreted as the exact solution of a nearby modified equation. Investigating the behaviour of numerical solutions by analysing the modified equation is known as backward…

The following document presents some novel numerical methods valid for one and several variables, which using the fractional derivative, allow to find solutions for some non-linear systems in the complex space using real initial conditions.…

Approximate Bayesian computation (ABC) methods have become increasingly prevalent of late, facilitating as they do the analysis of intractable, or challenging, statistical problems. With the initial focus being primarily on the practical…

Control-based continuation is technique for tracking the solutions and bifurcations of nonlinear experiments. The basic idea is to apply the method of numerical continuation to a feedback-controlled physical experiment. Since in an…

The central problem in electronic structure theory is the computation of the eigenvalues of the electronic Hamiltonian -- an unbounded, self-adjoint operator acting on a Hilbert space of antisymmetric functions. Coupled cluster (CC)…

A novel method rooted in the classical Schwarz-Christoffel transformation from the disk is introduced, which allows for fast and accurate solution of potential field problems in possibly inhomogeneous and multiply connected domains: this is…

Spectral Clustering(SC) is a prominent data clustering technique of recent times which has attracted much attention from researchers. It is a highly data-driven method and makes no strict assumptions on the structure of the data to be…

Four decades after their invention, quasi-Newton methods are still state of the art in unconstrained numerical optimization. Although not usually interpreted thus, these are learning algorithms that fit a local quadratic approximation to…

This article describes an approximation technique based on fractional order Bernstein wavelets for the numerical simulations of fractional oscillation equations under variable order, and the fractional order Bernstein wavelets are derived…

Quasi-Monte Carlo (QMC) methods are being adopted in statistical applications due to the increasingly challenging nature of numerical integrals that are now routinely encountered. For integrands with $d$-dimensions and derivatives of order…

We study the boundary asymptotics of ACH metrics which are formally Einstein. In terms of the partially integrable almost CR structure induced on the boundary at infinity, existence and uniqueness of such formal asymptotic expansions are…

A general quantum many-body theory in configuration space is developed by extending the traditional coupled cluter method (CCM) to a variational formalism. Two independent sets of distribution functions are introduced to evaluate the…

In many commercial and academic settings, numerical solvers fail to achieve their theoretical performance levels due to issues in the system definition, parameterization, and even implementation. We propose a pair of methods for detecting…