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The weighted version of the decision problem was one of Karp's 21 NP-complete problems; [11] Karp showed the NP-completeness by a reduction from the partition problem. The canonical optimization variant of the above decision problem is usually known as the Maximum-Cut Problem or Max-Cut and is defined as: Given a graph G, find a maximum cut.
If an equation can be put into the form f(x) = x, and a solution x is an attractive fixed point of the function f, then one may begin with a point x 1 in the basin of attraction of x, and let x n+1 = f(x n) for n ≥ 1, and the sequence {x n} n ≥ 1 will converge to the solution x.
The approximation of the square root of 2 is four sexagesimal figures, which is about six decimal figures. 1 + 24/60 + 51/60 2 + 10/60 3 = 1.41421296... [ 1 ] Numerical analysis is the study of algorithms that use numerical approximation (as opposed to symbolic manipulations ) for the problems of mathematical analysis (as distinguished from ...
A Fermi problem (or Fermi question, Fermi quiz), also known as an order-of-magnitude problem, is an estimation problem in physics or engineering education, designed to teach dimensional analysis or approximation of extreme scientific calculations. Fermi problems are usually back-of-the-envelope calculations.
There exist inputs to the travelling salesman problem that cause the Christofides algorithm to find a solution whose approximation ratio is arbitrarily close to 3/2. One such class of inputs are formed by a path of n vertices, with the path edges having weight 1 , together with a set of edges connecting vertices two steps apart in the path with ...
To use a finite difference method to approximate the solution to a problem, one must first discretize the problem's domain. This is usually done by dividing the domain into a uniform grid (see image). This means that finite-difference methods produce sets of discrete numerical approximations to the derivative, often in a "time-stepping" manner.
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