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2. Linear equation - Wikipedia

   en.wikipedia.org/wiki/Linear_equation

   Conversely, every line is the set of all solutions of a linear equation. The phrase "linear equation" takes its origin in this correspondence between lines and equations: a linear equation in two variables is an equation whose solutions form a line. If b ≠ 0, the line is the graph of the function of x that has been defined in the preceding ...

3. Gaussian elimination - Wikipedia

   en.wikipedia.org/wiki/Gaussian_elimination

   Once y is also eliminated from the third row, the result is a system of linear equations in triangular form, and so the first part of the algorithm is complete. From a computational point of view, it is faster to solve the variables in reverse order, a process known as back-substitution. One sees the solution is z = −1, y = 3, and x = 2. So ...

4. Signal-flow graph - Wikipedia

   en.wikipedia.org/wiki/Signal-flow_graph

   The systematic reduction of a linear signal-flow graph is a graphical method equivalent to the Gauss-Jordan elimination method for solving linear equations. [23] The rules presented below may be applied over and over until the signal flow graph is reduced to its "minimal residual form".

5. Linear algebra - Wikipedia

   en.wikipedia.org/wiki/Linear_algebra

   Systems of linear equations arose in Europe with the introduction in 1637 by René Descartes of coordinates in geometry. In fact, in this new geometry, now called Cartesian geometry, lines and planes are represented by linear equations, and computing their intersections amounts to solving systems of linear equations.

6. Flow graph (mathematics) - Wikipedia

   en.wikipedia.org/wiki/Flow_graph_(mathematics)

   A flow graph is a form of digraph associated with a set of linear algebraic or differential equations: [1] [2] "A signal flow graph is a network of nodes (or points) interconnected by directed branches, representing a set of linear algebraic equations. The nodes in a flow graph are used to represent the variables, or parameters, and the ...

7. Relaxation (iterative method) - Wikipedia

   en.wikipedia.org/wiki/Relaxation_(iterative_method)

   These equations describe boundary-value problems, in which the solution-function's values are specified on boundary of a domain; the problem is to compute a solution also on its interior. Relaxation methods are used to solve the linear equations resulting from a discretization of the differential equation, for example by finite differences. [2 ...