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In mathematics, linearization is finding the linear approximation to a function at a given point. The linear approximation of a function is the first order Taylor expansion around the point of interest. In the study of dynamical systems, linearization is a method for assessing the local stability of an equilibrium point of a system of nonlinear ...
In a linearizable system, although operations overlap on a shared object, each operation appears to take place instantaneously. Linearizability is a strong correctness condition, which constrains what outputs are possible when an object is accessed by multiple processes concurrently.
C3 superclass linearization is an algorithm used primarily to obtain the order in which methods should be inherited in the presence of multiple inheritance. In other words, the output of C3 superclass linearization is a deterministic Method Resolution Order (MRO). C3 superclass linearization is called C3 because it "is consistent with three ...
hide. In numerical analysis, the local linearization (LL) method is a general strategy for designing numerical integrators for differential equations based on a local (piecewise) linearization of the given equation on consecutive time intervals. The numerical integrators are then iteratively defined as the solution of the resulting piecewise ...
Feedback linearization is a common strategy employed in nonlinear control to control nonlinear systems. Feedback linearization techniques may be applied to nonlinear control systems of the form. where is the state, are the inputs. The approach involves transforming a nonlinear control system into an equivalent linear control system through a ...
Hartman–Grobman theorem. In mathematics, in the study of dynamical systems, the Hartman–Grobman theorem or linearisation theorem is a theorem about the local behaviour of dynamical systems in the neighbourhood of a hyperbolic equilibrium point. It asserts that linearisation —a natural simplification of the system—is effective in ...
Carleman linearization. In mathematics, Carleman linearization (or Carleman embedding) is a technique to transform a finite-dimensional nonlinear dynamical system into an infinite-dimensional linear system. It was introduced by the Swedish mathematician Torsten Carleman in 1932. [ 1] Carleman linearization is related to composition operator and ...
Linear approximation. Tangent line at (a, f (a)) In mathematics, a linear approximation is an approximation of a general function using a linear function (more precisely, an affine function). They are widely used in the method of finite differences to produce first order methods for solving or approximating solutions to equations.