Related papers: AAA-least squares rational approximation and solut…
In this paper, the discontinuous Petrov--Galerkin approximation of the Laplace eigenvalue problem is discussed. We consider in particular the primal and ultra weak formulations of the problem and prove the convergence together with a priori…
In this work, we study the problem of finding approximate, with minimum support set, solutions to matrix max-plus equations, which we call sparse approximate solutions. We show how one can obtain such solutions efficiently and in polynomial…
Developing efficient methods for solving parametric partial differential equations is crucial for addressing inverse problems. This work introduces a Least-Squares-based Neural Network (LS-Net) method for solving linear parametric PDEs. It…
We provide a randomized linear time approximation scheme for a generic problem about clustering of binary vectors subject to additional constrains. The new constrained clustering problem encompasses a number of problems and by solving it,…
Nonnegative (linear) least square problems are a fundamental class of problems that is well-studied in statistical learning and for which solvers have been implemented in many of the standard programming languages used within the machine…
We propose a new least squares finite element method to solve the Stokes problem with two sequential steps. The approximation spaces are constructed by patch reconstruction with one unknown per element. For the first step, we reconstruct an…
The classical Talbot method for the computation of the inverse Laplace transform is improved for the case where the transform is analytic in the complex plane except for the negative real axis. First, by using a truncated Talbot contour…
A mean field feedback artificial neural network algorithm is developed and explored for the set covering problem. A convenient encoding of the inequality constraints is achieved by means of a multilinear penalty function. An approximate…
In 1982, Lagarias showed that solving the approximate Shortest Vector Problem also solves the problem of finding good simultaneous Diophantine approximations. Here we provide a deterministic, dimension-preserving reduction in the reverse…
We present a simple yet accurate method to compute the adjoint double layer potential, which is used to solve the Neumann boundary value problem for Laplace's equation in three dimensions. An expansion in curvilinear coordinates leads us to…
Computing rational minimax approximations can be very challenging when there are singularities on or near the interval of approximation - precisely the case where rational functions outperform polynomials by a landslide. We show that far…
This work investigates the convergence behavior of augmented Lagrangian methods (ALMs) when applied to convex optimization problems that may be infeasible. ALMs are a popular class of algorithms for solving constrained optimization…
We present a rational filter for computing all eigenvalues of a symmetric definite eigenvalue problem lying in an interval on the real axis. The linear systems arising from the filter embedded in the subspace iteration framework, are solved…
A high-order quadrature scheme is constructed for the evaluation of Laplace single and double layer potentials and their normal derivatives on smooth surfaces in three dimensions. The construction begins with a harmonic approximation of the…
Penalized regression methods, such as $L_1$ regularization, are routinely used in high-dimensional applications, and there is a rich literature on optimality properties under sparsity assumptions. In the Bayesian paradigm, sparsity is…
The least squares method allows fitting parameters of a mathematical model from experimental data. This article proposes a general approach of this method. After introducing the method and giving a formal definition, the transitivity of the…
We consider the problem of finding the global optimum of a real-valued complex polynomial on a compact set defined by real-valued complex polynomial inequalities. It reduces to solving a sequence of complex semidefinite programming…
This chapter will appear in the forthcoming Handbook of Approximate Bayesian Computation (2018). The conceptual and methodological framework that underpins approximate Bayesian computation (ABC) is targetted primarily towards problems in…
Dual first-order methods are powerful techniques for large-scale convex optimization. Although an extensive research effort has been devoted to studying their convergence properties, explicit convergence rates for the primal iterates have…
Maximum Likelihood Estimation of continuous variable models can be very challenging in high dimensions, due to potentially complex probability distributions. The existence of multiple interdependencies among variables can make it very…