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The discharging method is used to prove that every graph in a certain class contains some subgraph from a specified list. The presence of the desired subgraph is then often used to prove a coloring result. [1] Most commonly, discharging is applied to planar graphs. Initially, a charge is assigned to each face and each vertex of the graph. The ...
Robot in a wooden maze. A maze-solving algorithm is an automated method for solving a maze.The random mouse, wall follower, Pledge, and Trémaux's algorithms are designed to be used inside the maze by a traveler with no prior knowledge of the maze, whereas the dead-end filling and shortest path algorithms are designed to be used by a person or computer program that can see the whole maze at once.
The associated method call expects the expression Z to be derived with regard to a variable V. The method returns a pair of the evaluated function and its derivative. The method traverses the expression tree recursively until a variable is reached. If the derivative with respect to this variable is requested, its derivative is 1, 0 otherwise.
Automata theory also studies the existence or nonexistence of any effective algorithms to solve problems similar to the following list: Does an automaton accept at least one input word? (Emptiness checking) Is it possible to transform a given non-deterministic automaton into a deterministic automaton without changing the language recognized?
This was the first automated deduction system to demonstrate an ability to solve mathematical problems that were announced in the Notices of the American Mathematical Society before solutions were formally published. [citation needed] First-order theorem proving is one of the most mature subfields of automated theorem proving. The logic is ...
Flowchart of using successive subtractions to find the greatest common divisor of number r and s. In mathematics and computer science, an algorithm (/ ˈ æ l ɡ ə r ɪ ð əm / ⓘ) is a finite sequence of mathematically rigorous instructions, typically used to solve a class of specific problems or to perform a computation. [1]
The iterative methods used to solve problems of nonlinear programming differ according to whether they evaluate Hessians, gradients, or only function values. While evaluating Hessians (H) and gradients (G) improves the rate of convergence, for functions for which these quantities exist and vary sufficiently smoothly, such evaluations increase ...
Epidemiological methods; Euler's forward method; Explicit and implicit methods (numerical analysis) Finite difference method (numerical analysis) Finite element method (numerical analysis) Finite volume method (numerical analysis) Highest averages method (voting systems) Method of exhaustion; Method of infinite descent (number theory ...