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Linear and non-linear equations. In the case of a single equation, the "solver" is more appropriately called a root-finding algorithm. Systems of linear equations. Nonlinear systems. Systems of polynomial equations, which are a special case of non linear systems, better solved by specific solvers. Linear and non-linear optimisation problems
Lis (Library of Iterative Solvers for linear systems; pronounced lis]) is a scalable parallel software library to solve discretized linear equations and eigenvalue problems that mainly arise from the numerical solution of partial differential equations using iterative methods.
The simplest method for solving a system of linear equations is to repeatedly eliminate variables. This method can be described as follows: In the first equation, solve for one of the variables in terms of the others. Substitute this expression into the remaining equations. This yields a system of equations with one fewer equation and unknown.
Conceived in 1937, the machine was built by Iowa State College mathematics and physics professor John Vincent Atanasoff with the help of graduate student Clifford Berry.It was designed only to solve systems of linear equations and was successfully tested in 1942.
Elemental is an open source software for distributed-memory dense and sparse-direct linear algebra and optimization. [49] HASEM is a C++ template library, being able to solve linear equations and to compute eigenvalues. It is licensed under BSD License. [50] LAMA
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 ...