Related papers: On a progressive and iterative approximation metho…
We propose a new modified primal-dual proximal best approximation method for solving convex not necessarily differentiable optimization problems. The novelty of the method relies on introducing memory by taking into account iterates…
We introduce an adaptive scattered data fitting scheme as extension of local least squares approximations to hierarchical spline spaces. To efficiently deal with non-trivial data configurations, the local solutions are described in terms of…
The modern ability to collect vast quantities of data poses a challenge for parameter estimation problems. When posed as a nonlinear least squares problem fitting a model to data, the cost of each iteration grows linearly with the amount of…
In many applications of tomography, the acquired projections are either limited in number or contain a significant amount of noise. In these cases, standard reconstruction methods tend to produce artifacts that can make further analysis…
We discuss local linear smooth backfitting for additive non-parametric models. This procedure is well known for achieving optimal convergence rates under appropriate smoothness conditions. In particular, it allows for the estimation of each…
Clinically useful proton Computed Tomography images will rely on algorithms to find the three-dimensional proton stopping power distribution that optimally fits the measured proton data. We present a least squares iterative method with many…
This work introduces a stochastic hierarchical optimization framework inspired by Sloppy Model theory for the efficient calibration of physical models. Central to this method is the use of a reduced Hessian approximation, which identifies…
A number of optimal decision problems with uncertainty can be formulated into a stochastic optimal control framework. The Least-Squares Monte Carlo (LSMC) algorithm is a popular numerical method to approach solutions of such stochastic…
We consider the problem of finding a sparse solution for an underdetermined linear system of equations when the known parameters on both sides of the system are subject to perturbation. This problem is particularly relevant to…
In many applications, it makes sense to solve the least square problems with nonnegative constraints. In this article, we present a new multiplicative iteration that monotonically decreases the value of the nonnegative quadratic programming…
A Multi-Layer Perceptron (MLP) defines a family of artificial neural networks often used in TS modeling and forecasting. Because of its "black box" aspect, many researchers refuse to use it. Moreover, the optimization (often based on the…
It is shown that the the popular least squares method of option pricing converges even under very general assumptions. This substantially increases the freedom of creating different implementations of the method, with varying levels of…
Projected least squares (PLS) is an intuitive and numerically cheap technique for quantum state tomography. The method first computes the least-squares estimator (or a linear inversion estimator) and then projects the initial estimate onto…
We propose to view non-rigid surface registration as a probabilistic inference problem. Given a target surface, we estimate the posterior distribution of surface registrations. We demonstrate how the posterior distribution can be used to…
Recurrent Neural Networks and in particular Long Short-Term Memory (LSTM) networks have demonstrated state-of-the-art accuracy in several emerging Artificial Intelligence tasks. However, the models are becoming increasingly demanding in…
Structured Low-Rank Approximation is a problem arising in a wide range of applications in Numerical Analysis and Engineering Sciences. Given an input matrix $M$, the goal is to compute a matrix $M'$ of given rank $r$ in a linear or affine…
We analyze an Iteratively Re-weighted Least Squares (IRLS) algorithm for promoting l1-minimization in sparse and compressible vector recovery. We prove its convergence and we estimate its local rate. We show how the algorithm can be…
A numerical method is developed to solve linear semi-infinite programming problem (LSIP) in which the iterates produced by the algorithm are feasible for the original problem. This is achieved by constructing a sequence of standard linear…
Purpose: To introduce a fast and improved direct reconstruction method for multi-shot diffusion weighted (msDW) scans for high-resolution studies. Methods:Multi-shot EPI methods can enable higher spatial resolution for diffusion MRI…
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…