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Recent advances in the use of remote labs in fluid mechanics
Published in Ataur Rahman, Vojislav Ilic, Blended Learning in Engineering Education, 2018
GNU Octave: GNU Octave was designed for numerical computations. Both linear and non-linear problems can be solved numerically using an interactive command-line interface. This is an open source redistributable software. Anyone using it can contribute to the development of GNU Octave by modifying it (Eaton et al., 1997). GNU Octave has been used by many researchers to design mathematical models for high-level numerical simulation.
Fourier and Laplace Transforms
Published in Russell L. Herman, An Introduction to Fourier Analysis, 2016
GNU Octave is a MATLAB clone which is free and open. It can be obtained from https://www.gnu.org/software/octave/. Many MATLAB m- files can be run in GNU Octave with little change. However, the symbolic package has to be installed.
QR decomposition for the least squares method: theory and practice
Published in International Journal of Mathematical Education in Science and Technology, 2022
The QR decomposition is a robust, relatively simple, and elegant procedure that requires only basic knowledge of calculus, linear algebra and computer programming to understand and implement it. However, its usage for the least squares problem solving and especially its practical implementation requires considering issues with avoidance of explicit formation of matrices for Givens rotations and Householder reflections. The resulting MATLAB or GNU Octave source code is rather easy to understand. It is even simpler than the traditional approach based on explicit generation of normal equations (Equation 2) and usage of Gaussian elimination because it doesn’t require a formation of the matrix and selection of pivot elements. The source code for Givens rotations is slightly longer than for Householder reflections. But it is easier to translate it into lower-level languages such as C, Pascal or Fortran because it doesn’t use such MATLAB subroutines as norm (2-norm of the vector), dot (dot product of two vectors) and doesn’t require allocation of buffers for u and v vectors.
Calculus of convex polyhedra and polyhedral convex functions by utilizing a multiple objective linear programming solver
Published in Optimization, 2019
Daniel Ciripoi, Andreas Löhne, Benjamin Weißing
Bensolve tools is a free and open source software for GNU Octave and Matlab. It utilizes the VLP solver bensolve [13], which is written in C programming language. The recent version of bensolve tools [12] has the following features: calculus of convex polyhedra,calculus of polyhedral convex function,solver for polyhedral convex programs (via LP reformulation),solver for vector linear programs and multiple objective linear programs (bensolve interface),solver for quasi-convace global optimization problems, see [14] for details.
Modelling a one retailer–one manufacturer supply chain system considering environmental sustainability and disruption
Published in International Journal of Systems Science: Operations & Logistics, 2021
Due to the complexity of the profit function, it is not possible to obtain an analytical solution or to show the concavity of the profit function analytically. For every given order (action) of the retailer to the manufacturer, the optimal raw material order or the optimal production quantity for the manufacturer is obtained numerically by using MATLAB. The obtained optimal production quantity is then used as an input parameter to build a Markov decision model of the retailer. The transition probability and the expected total profit of the retailer in a period are also computed using MATLAB. All possible actions corresponding to all possible states of the retailer are evaluated to obtain the optimal policy. The optimal policy or the optimal decision rule regarding the work order for the retailer is achieved using the MDP toolbox in MATLAB. The MDP toolbox (http://www7.inra.fr/mia/T/MDPtoolbox) recommends functions that are associated with the determination of discrete-time Markov decision processes: policy iteration, linear programming, and value iteration algorithms with some variations (Chadès et al., 2014). The MDP toolbox is accessible in several environments such as MATLAB, Scilab, R, and GNU Octave (Chadès et al., 2014). Once the optimal policy regarding the work order of the retailer in a sales horizon (n−1) is obtained for a selected G, the total expected profit of the retailer and the corresponding total expected profit of the manufacturer in a finite horizon (n) is also computed for the same G using MATLAB. The computation is repeated for every selected G until we obtain the optimal value of G and K for the manufacturer as well as the ultimate optimal policy of the retailer’s MDP model.