Topic
Linear approximation
About: Linear approximation is a research topic. Over the lifetime, 3901 publications have been published within this topic receiving 74764 citations.
Papers published on a yearly basis
Papers
More filters
TL;DR: A vector radiative transfer model for coupled atmosphere and ocean systems based on the Successive Order of Scattering (SOS) method has been developed for easy-to-use and computationally efficient as mentioned in this paper.
Abstract: A vector radiative transfer model has been developed for coupled atmosphere and ocean systems based on the Successive Order of Scattering (SOS) Method. The emphasis of this study is to make the model easy-to-use and computationally efficient. This model provides the full Stokes vector at arbitrary locations which can be conveniently specified by users. The model is capable of tracking and labeling different sources of the photons that are measured, e.g. water leaving radiances and reflected sky lights. This model also has the capability to separate florescence from multi-scattered sunlight. The δ - fit technique has been adopted to reduce computational time associated with the strongly forward-peaked scattering phase matrices. The exponential - linear approximation has been used to reduce the number of discretized vertical layers while maintaining the accuracy. This model is developed to serve the remote sensing community in harvesting physical parameters from multi-platform, multi-sensor measurements that target different components of the atmosphere-oceanic system.
110 citations
TL;DR: It is proved that linearizing the inverse problem of EIT does not lead to shape errors for piecewise-analytic conductivities and bounds are obtained on how well the linear reconstructions and the true conductivity difference agree on the boundary of the linearized equation.
Abstract: For electrical impedance tomography (EIT), the linearized reconstruction method using the Frechet derivative of the Neumann-to-Dirichlet map with respect to the conductivity has been widely used in the last three decades. However, few rigorous mathematical results are known regarding the errors caused by the linear approximation. In this work we prove that linearizing the inverse problem of EIT does not lead to shape errors for piecewise-analytic conductivities. If a solution of the linearized equations exists, then it has the same outer support as the true conductivity change, no matter how large the latter is. Under an additional definiteness condition we also show how to approximately solve the linearized equation so that the outer support converges toward the right one. Our convergence result is global and also applies for approximations by noisy finite-dimensional data. Furthermore, we obtain bounds on how well the linear reconstructions and the true conductivity difference agree on the boundary of t...
110 citations
TL;DR: In this article, a rigorous segment partition method was proposed to obtain a set of optimal segment points by minimizing the difference between chord and arc lengths, in order to derive a tighter piecewise linear approximation of QCCs and in turn a better UC solution as compared to the equipartition method.
Abstract: This letter provides a tighter piecewise linear approximation of generating units' quadratic cost curves (QCCs) for unit commitment (UC) problems. In order to facilitate the UC optimization process with efficient mixed-integer linear programing (MILP) solvers, QCCs are piecewise linearized for converting the original mixed-integer quadratic programming (MIQP) problem into an MILP problem. Traditionally, QCCs are piecewise linearized by evenly dividing the entire real power region into segments. This letter discusses a rigorous segment partition method for obtaining a set of optimal segment points by minimizing the difference between chord and arc lengths, in order to derive a tighter piecewise linear approximation of QCCs and, in turn, a better UC solution as compared to the equipartition method. Numerical test results show the effectiveness of the proposed method on a tighter piecewise linear approximation for better UC solutions.
110 citations
TL;DR: Birch's law arises in the physics of solids as a linear approximation, in a certain range of density, of a power law for a change of chemical composition within the same crystal structure.
Abstract: Birch9s law arises in the physics of solids as a linear approximation, in a certain range of density, of a power law. For a change of chemical composition within the same crystal structure, the velocity-density relation is constant with a slope of nearly -0.5 in the first-order approximation.
109 citations
TL;DR: In this article, the P-N differential approximation was used to predict emissive power distributions and heat transfer rates in two-dimensional media with opacities of unity or greater.
Abstract: Radiative energy transfer in a gray absorbing and emitting medium is considered in a two-dimensional rectangular enclosure using the P-N differential approximation approximation. The two-dimensional moment of intensity partial differential equations (PDE's) are combined to yield a single second-order PDE for the P-1 approximation and four coupled second-order PDE's for the P-3 approximation. P-1 approximation results are obtained from separation of variables solutions, and P-3 results are obtained numerically using successive-over-relaxation methods. The P-N approximation results are compared with numerical Hottel zone results and with results from an approximation method developed by Modest. The studies show that the P-3 approximation can be used to predict emissive power distributions and heat transfer rates in two-dimensional media with opacities of unity or greater. The P-1 approximation is identical to the diffusion solution and is thus applicable only if the medium is optically dense.
109 citations