Non-Linear Equation
(Redirected from Nonlinear Algebraic Equation)
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A Non-Linear Equation is an algebraic equation that ...
- AKA: Nonlinear Algebraic Equation.
- Example(s):
- a Polynomial Equation, such as a quadratic equation.
- an Exponential Equation.
- …
- Counter-Example(s):
- See: Nonlinear System, Linear System, Differential Equation, Root-Finding Algorithm, Algebraic Geometry.
References
2015
- (Wikipedia, 2015) ⇒ http://en.wikipedia.org/wiki/nonlinear_system#Nonlinear_algebraic_equations Retrieved:2015-10-31.
- Nonlinear algebraic equations, which are also called polynomial equations, are defined by equating polynomials to zero. For example, : [math]\displaystyle{ x^2 + x - 1 = 0\,. }[/math] For a single polynomial equation, root-finding algorithms can be used to find solutions to the equation (i.e., sets of values for the variables that satisfy the equation). However,
systems of algebraic equations are more complicated; their study is one motivation for the field of algebraic geometry, a difficult branch of modern mathematics. It is even difficult to decide whether a given algebraic system has complex solutions (see Hilbert's Nullstellensatz). Nevertheless, in the case of the systems with a finite number of complex solutions, these systems of polynomial equations are now well understood and efficient methods exist for solving them.
- Nonlinear algebraic equations, which are also called polynomial equations, are defined by equating polynomials to zero. For example, : [math]\displaystyle{ x^2 + x - 1 = 0\,. }[/math] For a single polynomial equation, root-finding algorithms can be used to find solutions to the equation (i.e., sets of values for the variables that satisfy the equation). However,