 Level Set 546 浏览 0关注

In mathematics, a level set of a real number|real-valued function (mathematics)|function f of n variables is a set of the form : L_c(f) = \left\{ (x_1, \cdots, x_n) \, \mid \, f(x_1, \cdots, x_n) = c \right\}~,that is, a set where the function takes on a given constant value c. When the number of variables is two, a level set is generically a curve, called a level curve, contour line, or isoline. When n&nbsp;=&nbsp;3, a level set is called a level surface (see also isosurface), and for higher values of n the level set is a level hypersurface.A set of the form : L_c^-(f) = \left\{ (x_1, \cdots, x_n) \, \mid \, f(x_1, \cdots, x_n) \leq c \right\}is called a sublevel set of f (or, alternatively, a lower level set or trench of f).: L_c^+(f) = \left\{ (x_1, \cdots, x_n) \, \mid \, f(x_1, \cdots, x_n) \geq c \right\}is called a superlevel set of f. A level set is a special case of a fiber (mathematics)|fiber.
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Level Set文章数量变化趋势 