|
Quasilinearization
In mathematics, quasilinearization is a technique which replaces a nonlinear differential equation or operator equation (or system of such equations) with a sequence of linear problems, which are presumed to be easier, and whose solutions approximate the solution of the original nonlinear problem with increasing accuracy. It is a generalization of Newton's method; the word "quasilinearization" is commonly used when the differential equation is a boundary value problem. Abstract formulation Quasilinearization replaces a given nonlinear operator with a certain linear operator which, being simpler, can be used in an iterative fashion to approximately solve equations containing the original nonlinear operator. This is typically performed when trying to solve an equation such as together with certain boundary conditions for which the equation has a solution . This solution is sometimes called the "reference solution". For quasilinearization to work, the reference solution needs to ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Nonlinear Operator
In mathematics, and more specifically in linear algebra, a linear map (also called a linear mapping, linear transformation, vector space homomorphism, or in some contexts linear function) is a mapping V \to W between two vector spaces that preserves the operations of vector addition and scalar multiplication. The same names and the same definition are also used for the more general case of modules over a ring; see Module homomorphism. If a linear map is a bijection then it is called a . In the case where V = W, a linear map is called a linear endomorphism. Sometimes the term refers to this case, but the term "linear operator" can have different meanings for different conventions: for example, it can be used to emphasize that V and W are real vector spaces (not necessarily with V = W), or it can be used to emphasize that V is a function space, which is a common convention in functional analysis. Sometimes the term ''linear function'' has the same meaning as ''linear map'', ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
