Search results for "linear equations"
showing 10 items of 64 documents
Two optimizing procedures for the solution of complex systems of equations: a powerful tool for modelling and simulation of metabolism
2000
Introduction Standard calculations for the evaluation of indirect calorimetry (IC) are based on two-dimensional nonlinear systems of equations. For a more sophisticated evaluation metabolic models can be used, which are described by complex systems of equations. Since the solutions are multidimensional, a concrete result must be selected by means of constraints, using optimizing procedures. These multidimensional optimizations are critical concerning processing time and reproducibility of minimum detection. Methods In order to simulate the status of metabolism of ICU patients on the basis of IC data, a complex model of metabolism was developed. The model was described by a system of equatio…
Functional design of power-split CVTs: An uncoupled hierarchical optimized model
2017
Abstract This paper provides a new model for the preliminary design of compound power-split CVTs. Unlike the existing models, the presented method allows the engineers to prioritize functionality and efficiency of the transmission, while delaying the choice of the involved gear sets’ layout as long as possible. The design approach follows a specific priority order, and each step deals with one particular issue, without mutual interference. A smart design-chart eases the assessment and the comparison of the only eligible alternatives, and eventually leads to a final feasible constructive scheme, which can be an excellent concept for further optimization and implementation. Moreover, the mode…
A class of quasi-Newton generalized Steffensen methods on Banach spaces
2002
AbstractWe consider a class of generalized Steffensen iterations procedure for solving nonlinear equations on Banach spaces without any derivative. We establish the convergence under the Kantarovich–Ostrowski's conditions. The majorizing sequence will be a Newton's type sequence, thus the convergence can have better properties. Finally, a numerical comparation with the classical methods is presented.
The Kp Hierarchy
1989
As an application of the theory of infinite-dimensional Grassmannians and the representation theory of gl1 we shall study in this chapter certain nonlinear “exactly solvable” systems of differential equations. Exactly solvable means here that the nonlinear system can be transformed to an (infinite-dimensional) linear problem. A prototype of the equations is the Korteweg-de Vries equation $$\frac{{\partial u}}{{\partial t}} = \frac{3}{3}u\frac{{\partial u}}{{\partial x}} + \frac{1}{4}\frac{{{\partial ^3}u}}{{\partial {x^3}}}$$ . It turns out that it is more natural to consider an infinite system of equations like that above, for obtaining explicit solutions. The set of equations is called th…
An improved five-parameter model for photovoltaic modules
2010
This paper presents a new five-parameter model capable of analytically describing the I–V characteristic of a photovoltaic module for each generic condition of operative temperature and solar irradiance. The parameters of the equivalent electrical circuit are extracted by solving a system of equations based on data commonly issued by manufacturers in standard rating conditions with a trial and error process. The procedure, which does not require any special equations solver, can be easily coded into a short software routine using simple languages and finds the solution of the system of equations with the desired accuracy without needing to be guided towards solutions starting from fitted in…
Springs-based Simulation for Image Retargeting
2011
In this paper an efficient method for image retargeting is pro- posed. It relies onto a mechanical model based on springs network. Each pixel displacement (compression or expan- sion) is given by the network response, according to the springs stiffness. The properties of the springs are deter- mined as function of the visual relevance of the pixels. Such model does not require any optimization, since its so- lution is obtained simply from a linear system of equations, allowing real-time application even for large images. The approach is fully automatic, though can be improved by interactively providing cues such as geometric constraints and/or manual relevant object labeling. The results pr…
Quantum graphs with mixed dynamics: the transport/diffusion case
2013
We introduce a class of partial differential equations on metric graphs associated with mixed evolution: on some edges we consider diffusion processes, on other ones transport phenomena. This yields a system of equations with possibly nonlocal couplings at the boundary. We provide sufficient conditions for these to be governed by a contractive semigroup on a Hilbert space naturally associated with the system. We show that our setting is also adequate to discuss specific systems of diffusion equations with boundary delays.
Influence of data input in the evaluation of Stress Intensity Factors from Thermoelastic Stress Analysis
2021
Abstract Thermoelastic Stress Analysis (TSA) is applied to evaluate the Stress Intensity Factor (SIF), T-stress and J-Integral in a Single-Edge-Notched-Tension sample undergoing fatigue cycling. The Williams’ series stress formulation and a least-square fitting (LSF) procedure are used to obtain the SIF and the T-stress. The evaluation is carried out with the aim to investigate the influence of the input data in the system of equations solved with the LSF, and in particular: the number of coefficients used in the Williams’ series and the choice and position of the fitted experimental data points. Three algorithms for the determination of the crack tip position are also evaluated: a coarse g…
Cluster Algorithm Integrated with Modification of Gaussian Elimination to Solve a System of Linear Equations
2020
The data accumulation and their inhomogeneous distribution lead to the issue of large and sparse systems solving in various fields: industrials, emergency management, etc. Complex structure in the data error creates additional risk to obtain an adequate solution. To facilitate problem-solving, we describe the technique that is based on intellectual division of data with following application of cluster algorithm and the modification of Gaussian elimination to different portions of data. In this paper, we present results of developed technique that was applied to samples of synthetic and real data. We compare them with outcomes of other algorithms (intelligence and classical) by using of num…
Systems of quasilinear elliptic equations with dependence on the gradient via subsolution-supersolution method
2017
For the homogeneous Dirichlet problem involving a system of equations driven by \begin{document}$(p,q)$\end{document} -Laplacian operators and general gradient dependence we prove the existence of solutions in the ordered rectangle determined by a subsolution-supersolution. This extends the preceding results based on the method of subsolution-supersolution for systems of elliptic equations. Positive and negative solutions are obtained.