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  2. System of linear equations - Wikipedia

    en.wikipedia.org/wiki/System_of_linear_equations

    In mathematics, a system of linear equations (or linear system) is a collection of two or more linear equations involving the same variables. [1][2] For example, is a system of three equations in the three variables x, y, z. A solution to a linear system is an assignment of values to the variables such that all the equations are simultaneously ...

  3. System of equations - Wikipedia

    en.wikipedia.org/wiki/System_of_equations

    System of equations. In mathematics, a set of simultaneous equations, also known as a system of equations or an equation system, is a finite set of equations for which common solutions are sought. An equation system is usually classified in the same manner as single equations, namely as a: System of linear equations, System of nonlinear equations,

  4. Gauss–Seidel method - Wikipedia

    en.wikipedia.org/wiki/Gauss–Seidel_method

    Gauss–Seidel method. In numerical linear algebra, the Gauss–Seidel method, also known as the Liebmann method or the method of successive displacement, is an iterative method used to solve a system of linear equations. It is named after the German mathematicians Carl Friedrich Gauss and Philipp Ludwig von Seidel.

  5. System of polynomial equations - Wikipedia

    en.wikipedia.org/wiki/System_of_polynomial_equations

    System of polynomial equations. A system of polynomial equations (sometimes simply a polynomial system) is a set of simultaneous equations f1 = 0, ..., fh = 0 where the fi are polynomials in several variables, say x1, ..., xn, over some field k. A solution of a polynomial system is a set of values for the xi s which belong to some algebraically ...

  6. Simultaneous equations model - Wikipedia

    en.wikipedia.org/wiki/Simultaneous_equations_model

    Simultaneous equations models are a type of statistical model in which the dependent variables are functions of other dependent variables, rather than just independent variables. [ 1 ] This means some of the explanatory variables are jointly determined with the dependent variable, which in economics usually is the consequence of some underlying ...

  7. Jacobi method - Wikipedia

    en.wikipedia.org/wiki/Jacobi_method

    Jacobi method. In numerical linear algebra, the Jacobi method (a.k.a. the Jacobi iteration method) is an iterative algorithm for determining the solutions of a strictly diagonally dominant system of linear equations. Each diagonal element is solved for, and an approximate value is plugged in. The process is then iterated until it converges.

  8. Runge–Kutta methods - Wikipedia

    en.wikipedia.org/wiki/Runge–Kutta_methods

    t. e. In numerical analysis, the Runge–Kutta methods (English: / ˈrʊŋəˈkʊtɑː / ⓘ RUUNG-ə-KUUT-tah[1]) are a family of implicit and explicit iterative methods, which include the Euler method, used in temporal discretization for the approximate solutions of simultaneous nonlinear equations. [2]

  9. Linear algebra - Wikipedia

    en.wikipedia.org/wiki/Linear_algebra

    The blue line is the common solution to two of these equations. Linear algebra is the branch of mathematics concerning linear equations such as: linear maps such as: and their representations in vector spaces and through matrices. [1][2][3] Linear algebra is central to almost all areas of mathematics. For instance, linear algebra is fundamental ...

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