A solver is a generic term indicating a piece of mathematical software, possibly in the form of a stand-alone computer program or as asoftware library, that ‘solves’ a mathematical problem. A solver takes problem descriptions in some sort of generic form and calculate their solution. In a solver, the emphasis is on creating a program or library that can easily be applied to other problems of similar type.
Types of problems with existing dedicated solvers include:
- 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
- Systems of ordinary differential equations
- Systems of differential algebraic equations
- Logic/satisfiability problems
- Constraint satisfaction problems
- Shortest path problems
- Minimum spanning tree problems
- Search algorithms
The General Problem Solver (GPS) is a particular computer program created in 1957 by Herbert Simon, J.C. Shaw, and Allen Ne-well intended to work as a universal problem solver, that theoretically can be used to solve every possible problem that can be formalized in a symbolic system, given the right input configuration. It was the first computer program which separated its knowledge of problems (in the form of domain rules) from its strategy of how to solve problems (as a general search engine).
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