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By using the dual form of this constraint optimization problem, it can be used to calculate the gradient very fast. A nice property is that the number of computations is independent of the number of parameters for which you want the gradient. The adjoint method is derived from the dual problem [4] and is used e.g. in the Landweber iteration ...
The grade (US) or gradient (UK) (also called stepth, slope, incline, mainfall, pitch or rise) of a physical feature, landform or constructed line is either the elevation angle of that surface to the horizontal or its tangent.
Mathematical expressions involving these quantities in vector calculus and tensor analysis (such as the gradient, divergence, curl, and Laplacian) can be transformed from one coordinate system to another, according to transformation rules for scalars, vectors, and tensors. Such expressions then become valid for any curvilinear coordinate system.
Stake. Gradient maps are both at the center and at the basic level of map making on Wikipedia. A simple blank map and fill with color tool are needed. To continue to build a coherent Wikipedia display, this page suggests the most suitable SVG source files together with a blue-based color ramps from academic, screen friendly, print friendly, and color-blind friendly ColorBrewer2 by cartography ...
Slope illustrated for y = (3/2)x − 1.Click on to enlarge Slope of a line in coordinates system, from f(x) = −12x + 2 to f(x) = 12x + 2. The slope of a line in the plane containing the x and y axes is generally represented by the letter m, [5] and is defined as the change in the y coordinate divided by the corresponding change in the x coordinate, between two distinct points on the line.
In principle, it is the angle between the gradient vector and the horizontal plane, given either as an angular measure α (common in scientific applications) or as the ratio =, commonly expressed as a percentage, such that p = tan α. The latter is frequently used in engineering applications like road and railway construction.
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A spatial gradient is a gradient whose components are spatial derivatives, i.e., rate of change of a given scalar physical quantity with respect to the position coordinates in physical space. Homogeneous regions have spatial gradient vector norm equal to zero.