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Reduction of order (or d’Alembert reduction) is a technique in mathematics for solving second-order linear ordinary differential equations. It is employed when one solution is known and a second linearly independent solution is desired. The method also applies to n -th order equations. In this case the ansatz will yield an (n −1)-th order ...
Model order reduction. Model order reduction (MOR) is a technique for reducing the computational complexity of mathematical models in numerical simulations. As such it is closely related to the concept of metamodeling, with applications in all areas of mathematical modelling.
In mathematics, a well-order (or well-ordering or well-order relation) on a set S is a total ordering on S with the property that every non-empty subset of S has a least element in this ordering. The set S together with the ordering is then called a well-ordered set .
Partial orders. A reflexive, weak, [1] or non-strict partial order, [2] commonly referred to simply as a partial order, is a homogeneous relation ≤ on a set that is reflexive, antisymmetric, and transitive. That is, for all it must satisfy: Reflexivity: , i.e. every element is related to itself.
Partial order reduction. In computer science, partial order reduction is a technique for reducing the size of the state-space to be searched by a model checking or automated planning and scheduling algorithm. It exploits the commutativity of concurrently executed transitions that result in the same state when executed in different orders.
A first-order reduction is a reduction where each component is restricted to be in the class FO of problems calculable in first-order logic . Since we have , the first-order reductions are stronger reductions than the logspace reductions . Many important complexity classes are closed under first-order reductions, and many of the traditional ...
Reduction operator. (Redirected from Reduction Operator) In computer science, the reduction operator[1] is a type of operator that is commonly used in parallel programming to reduce the elements of an array into a single result. Reduction operators are associative and often (but not necessarily) commutative. [2][3][4] The reduction of sets of ...
Formal definitions. Formally, a binary relation (→) on the set of terms is called a rewrite relation if it is closed under contextual embedding and under instantiation; formally: if l → r implies u [ l σ] p → u [ r σ] p for all terms l, r, u, each path p of u, and each substitution σ. If (→) is also irreflexive and transitive, then ...