Search results
Results from the WOW.Com Content Network
More generally, the same approach can be used to provide an implicit representation for graphs with bounded arboricity or bounded degeneracy, including the planar graphs and the graphs in any minor-closed graph family. [8] [9] Intersection graphs An interval graph is the intersection graph of a set of line segments in the real line.
The unit circle can be specified as the level curve f(x, y) = 1 of the function f(x, y) = x 2 + y 2.Around point A, y can be expressed as a function y(x).In this example this function can be written explicitly as () =; in many cases no such explicit expression exists, but one can still refer to the implicit function y(x).
In any case below all necessary differential conditions are presupposed. The determination of intersection points always leads to one or two non-linear equations which can be solved by Newton iteration. A list of the appearing cases follows: intersection of a parametric curve and an implicit curve intersection of two implicit curves
However, the implicit function theorem gives conditions under which an implicit curve locally is given by the graph of a function (so in particular it has no self-intersections). If the defining relations are sufficiently smooth then, in such regions, implicit curves have well defined slopes, tangent lines, normal vectors, and curvature.
Explicit and implicit methods are approaches used in numerical analysis for obtaining numerical approximations to the solutions of time-dependent ordinary and partial differential equations, as is required in computer simulations of physical processes.
In numerical analysis and scientific computing, the backward Euler method (or implicit Euler method) is one of the most basic numerical methods for the solution of ordinary differential equations. It is similar to the (standard) Euler method , but differs in that it is an implicit method .
Although this is defined using a particular coordinate system, the transformation law relating the ξ i and the x i ensures that σ P is a well-defined function on the cotangent bundle. The function σ P is homogeneous of degree k in the ξ variable. The zeros of σ P, away from the zero section of T ∗ X, are the characteristics of P.
In numerical analysis, fixed-point iteration is a method of computing fixed points of a function.. More specifically, given a function defined on the real numbers with real values and given a point in the domain of , the fixed-point iteration is + = (), =,,, … which gives rise to the sequence,,, … of iterated function applications , (), (()), … which is hoped to converge to a point .