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Quantum order-finding subroutine. The goal of the quantum subroutine of Shor's algorithm is, given coprime integers and , to find the order of modulo , which is the smallest positive integer such that . To achieve this, Shor's algorithm uses a quantum circuit involving two registers. The second register uses qubits, where is the smallest ...
Householder's method is a numerical algorithm for solving the equation f(x) = 0. In this case, the function f has to be a function of one real variable. The method consists of a sequence of iterations. beginning with an initial guess x0.
In mathematics, the order of a finite group is the number of its elements. If a group is not finite, one says that its order is infinite. The order of an element of a group (also called period length or period) is the order of the subgroup generated by the element. If the group operation is denoted as a multiplication, the order of an element a ...
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The leading-order behaviour is more complicated when more terms are leading-order. At x=2 there is a leading-order balance between the cubic and linear dependencies of y on x. Note that this description of finding leading-order balances and behaviours gives only an outline description of the process – it is not mathematically rigorous.
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Topological sorting. In computer science, a topological sort or topological ordering of a directed graph is a linear ordering of its vertices such that for every directed edge (u,v) from vertex u to vertex v, u comes before v in the ordering. For instance, the vertices of the graph may represent tasks to be performed, and the edges may ...
Muller's method is a root-finding algorithm, a numerical method for solving equations of the form f ( x) = 0. It was first presented by David E. Muller in 1956. Muller's method is based on the secant method, which constructs at every iteration a line through two points on the graph of f. Instead, Muller's method uses three points, constructs ...