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This paper presents a novel shooting method for solving two-point boundary value problems for second order ordinary differential equations. The method works as follows: first, a guess for the initial condition is made and an integration of…

In a transformation method, the numerical solution of a given boundary value problem is obtained by solving one or more related initial value problems. Therefore, a transformation method, like a shooting method, is an initial value method.…

Projection-based iterative methods for solving large over-determined linear systems are well-known for their simplicity and computational efficiency. It is also known that the correct choice of a sketching procedure (i.e., preprocessing…

In this article we study the problem of recovering the unknown solution of a linear ill-posed problem, via iterative regularization methods. We review the problem of projection-regularization from a statistical point of view. A basic…

Boundary value problems in ODEs arise in modelling many physical situations from microscale to mega scale. Such two-point boundary value problems (BVPs) are complex and often possess no analytical closed form solutions. So, one has to rely…

Projected Gradient Descent denotes a class of iterative methods for solving optimization programs. Its applicability to convex optimization programs has gained significant popularity for its intuitive implementation that involves only…

In computer vision, many problems such as image segmentation, pixel labelling, and scene parsing can be formulated as binary quadratic programs (BQPs). For submodular problems, cuts based methods can be employed to efficiently solve…

We study a fixed point iterative method based on generalized relaxation of strictly quasi-nonexpansive operators. The iterative method is assembled by averaging of strings, and each string is composed of finitely many strictly…

We present a novel deep learning approach to approximate the solution of large, sparse, symmetric, positive-definite linear systems of equations. These systems arise from many problems in applied science, e.g., in numerical methods for…

Many challenging tasks in sensor networks, including sensor calibration, ranking of nodes, monitoring, event region detection, collaborative filtering, collaborative signal processing, {\em etc.}, can be formulated as a problem of solving a…

This paper considers approximate smoothing for discretely observed non-linear stochastic differential equations. The problem is tackled by developing methods for linearising stochastic differential equations with respect to an arbitrary…

We introduce an iterative method to solve problems in small-strain non-linear elasticity, termed ``Phase-Space Iterations'' (PSIs). The method is inspired by recent work in data-driven computational mechanics, which reformulated the classic…

Probabilistic ideas and tools have recently begun to permeate into several fields where they had traditionally not played a major role, including fields such as numerical linear algebra and optimization. One of the key ways in which these…

We address the problem of epipolar geometry using the motion of silhouettes. Such methods match epipolar lines or frontier points across views, which are then used as the set of putative correspondences. We introduce an approach that…

Many inverse problems involve two or more sets of variables that represent different physical quantities but are tightly coupled with each other. For example, image super-resolution requires joint estimation of the image and motion…

The shooting method is used to solve a boundary value problem with separated and explicit constraints. To obtain approximations of an unknown initial values there are considered arguments based on the adjoint differential system attached to…

Recently, an approach known as relaxation has been developed for preserving the correct evolution of a functional in the numerical solution of initial-value problems, using Runge-Kutta methods. We generalize this approach to multistep…

This paper introduces a family of iterative algorithms for unconstrained nonlinear optimal control. We generalize the well-known iLQR algorithm to different multiple-shooting variants, combining advantages like straight-forward…

We propose an iterative method for nonlinear semidefinite programs with box constraints. The search direction in the proposed method utilizes the distance from the current point to the boundary of a feasible set. The computation of the…

We shed new light on the \textit{smoothness} of optimization problems arising in prediction error parameter estimation of linear and nonlinear systems. We show that for regions of the parameter space where the model is not contractive, the…