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Difference Map Algorithm
The difference-map algorithm is a search algorithm for general constraint satisfaction problems. It is a meta-algorithm in the sense that it is built from more basic algorithms that perform Projection (linear algebra), projections onto Constraint (mathematics), constraint sets. From a mathematical perspective, the difference-map algorithm is a dynamical system based on a Map (mathematics), mapping of Euclidean space. Solutions are encoded as Fixed point (mathematics), fixed points of the mapping. Although originally conceived as a general method for solving the phase problem, the difference-map algorithm has been used for the boolean satisfiability problem, protein structure prediction, Ramsey numbers, diophantine equations, and ''Sudoku'', as well as sphere- and disk-packing problems. Since these applications include NP-complete problems, the scope of the difference map is that of an incomplete algorithm. Whereas incomplete algorithms can efficiently verify solutions (once a candi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Iterations 0, 100, 200, 300 And 400 In Difference-map Reconstruction Of Grayscale Image From Fourier Transform Modulus
Iteration is the repetition of a process in order to generate a (possibly unbounded) sequence of outcomes. Each repetition of the process is a single iteration, and the outcome of each iteration is then the starting point of the next iteration. In mathematics and computer science, iteration (along with the related technique of recursion) is a standard element of algorithms. Mathematics In mathematics, iteration may refer to the process of iterated function, iterating a function, i.e. applying a function repeatedly, using the output from one iteration as the input to the next. Iteration of apparently simple functions can produce complex behaviors and difficult problems – for examples, see the Collatz conjecture and juggler sequences. Another use of iteration in mathematics is in iterative methods which are used to produce approximate numerical solutions to certain mathematical problems. Newton's method is an example of an iterative method. Manual calculation of a number's s ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |