Convex combination of alternating projection and Douglas–Rachford operators for phase retrieval

We present the convergence analysis of convex combination of the alternating projection and Douglas–Rachford operators for solving the phase retrieval problem. New convergence criteria for iterations generated by the algorithm are established by applying various schemes of numerical analysis and exploring both physical and mathematical...

Towards a general framework for fast and feasible k-space trajectories for MRI based on projection methods

The design of feasible trajectories to traverse the k-space for sampling in magnetic resonance imaging (MRI) is important while considering ways to reduce the scan time. Over the recent years, non-Cartesian trajectories have been observed to result in benign artifacts and being less sensitive to motion. In this paper, we propose a generalized...

Machine Learning with Care: Introducing a Machine Learning Project Method

Worldwide, machine learning is increasingly used to achieve optimal analytics and outcomes in business and governmental organisations. However, it has become evident that structural guidance for creating machine learning projects is needed. Machine learning projects are dependent on multiple factors. This thesis focuses on three factors...

A method for estimating fisheye lens’ field-of view angle and projection for HDR luminance capture

The calculation of field-of-view luminance based metrics for visual discomfort from glare evaluation in real scenes via HDR (High Dynamic Range) luminance capture does generally require the use of wide view fisheye lenses. This paper presents an easy to implement and low-cost method to estimate a fisheye lens’ total field-of view and projection...

A convergent relaxation of the Douglas–Rachford algorithm

This paper proposes an algorithm for solving structured optimization problems, which covers both the backward–backward and the Douglas–Rachford algorithms as special cases, and analyzes its convergence. The set of fixed points of the corresponding operator is characterized in several cases. Convergence criteria of the algorithm in terms of...

A NURBS based Galerkin projection method for the numerical computation of nonlinear normal modes using invariant manifolds

In this report a NURBS based Galerkin projection method will be synthesised for the numerical computation of nonlinear normal modes using invariant manifolds. The computed nonlinear normal modes will be used to create a reduced order model that describes the single mode dynamical behaviour of a nonlinear vibrational dynamical system. The...

PIDR(s): IDR(s) as a Projection Method

The Induced Dimension Reduction(s) method (or the IDR(s) method) is an example of an iterative method used for solving systems of linear equations. Projection methods are a special type of iterative method. They find an approximate solution in a subspace (the right subspace) by requiring that the residual is orthogonal to another subspace (the...

Direct gradient projection method with transformation of variables technique for structural topology optimization

This paper proposes an efficient and reliable topology optimization method that can obtain a black and white solution with a low objective function value within a few tens of iterations. First of all, a transformation of variables technique is adopted to eliminate the constraints on the design variables. After that, the optimization problem is...

Flame front capturing/tracking schemes for compressible and incompressible reactive flow

We present hybrid capturing/tracking methods for the simulation of turbulent premixed flames in meso- and large-scale geometries. Such schemes resemble a tracking schemes in that the flame front is explicitly computed and propagated using a level set method. The flame-flow-coupling uses in-cell-reconstruction. In cut cells, burnt and unburned...

A three-dimensional finite volume method for incompressible Navier-Stokes equations on unstructured hybrid staggered grids

In this work, a new method was described for spatial discretization of threedimensional Navier Stokes equations in their primitive form, on unstructured, staggered grids. Velocities were placed on the cell faces and pressure in cell centers and were linked with the projection method. Thanks to the variable arrangement, no stabilization procedure...