Linked Data Explorer
Formulation of linear problems and solution by a universal machine
Conversely, we show that for each ordered field algorithm there is a linear problem which the ordered field algorithm solves uniquely. Finally, it is shown that with an ordered field algorithm for a linear problem, one can solve certain parametric instances of the linear problem."
- "Conversely, we show that for each ordered field algorithm there is a linear problem which the ordered field algorithm solves uniquely. Finally, it is shown that with an ordered field algorithm for a linear problem, one can solve certain parametric instances of the linear problem.""@en
- "Abstract: "Using the predicate language for ordered fields we define a class of problems to which we refer as linear problems. This class contains, for example, all systems of linear equations and inequalities, all linear programming problems, all integer programming problems with bounded variables, all linear complementarity problems, the rank-computation of matrices, the testing of whether sets that are defined by linear inequalities are semi-lattices, all satisfiability problems in sentenial logic, all problems of determining complete simplices on a complex and all quadratic programming problems with bounded variables and all problems of computing row-reduced echelon forms of matrices."@en
- "We describe a single, one, method, to which we refer as the Univeral Linear Machine, which can be used to solve any instance of any linear problem. The Universal Linear Machine runs in two phases. Given a linear problem, in the first phase a Compiler running on a Turing Machine generates an ordered field algorithm for the problem. Then, given an instance of the linear problem, in the second phase the ordered field algorithm solves the particular instance of the linear problem. The ordered field algorithm is finite, deterministic, loopless and executes only the five ordered field operations -- additions, multiplications, subtractions, divisions and comparisons."@en
- "Formulation of linear problems and solution by a universal machine"
- "Formulation of linear problems and solution by a universal machine"@en