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Computing the square root of 2 (which is roughly 1.41421) is a well-posed problem.Many algorithms solve this problem by starting with an initial approximation x 0 to , for instance x 0 = 1.4, and then computing improved guesses x 1, x 2, etc.
Turbo coding is an iterated soft-decoding scheme that combines two or more relatively simple convolutional codes and an interleaver to produce a block code that can perform to within a fraction of a decibel of the Shannon limit.
The analysis of errors computed using the global positioning system is important for understanding how GPS works, and for knowing what magnitude errors should be expected. The Global Positioning System makes corrections for receiver clock errors and other effects but there are still residual errors which are not corrected.
The first pass goes forward in time while the second goes backward in time; hence the name forward–backward algorithm. The term forward–backward algorithm is also used to refer to any algorithm belonging to the general class of algorithms that operate on sequence models in a forward–backward manner. In this sense, the descriptions in the ...
The general algorithm involves message passing and is substantially similar to the belief propagation algorithm (which is the generalization of the forward-backward algorithm). With an algorithm called iterative Viterbi decoding, one can find the subsequence of an observation that matches best (on average) to a given hidden Markov model.
Reducing ε can be done at the cost of CPU time. Near-optimal erasure codes trade correction capabilities for computational complexity: practical algorithms can encode and decode with linear time complexity. Fountain codes (also known as rateless erasure codes) are notable examples of near-optimal erasure codes.
Reverse accumulation is more efficient than forward accumulation for functions f : R n → R m with n ≫ m as only m sweeps are necessary, compared to n sweeps for forward accumulation. Backpropagation of errors in multilayer perceptrons, a technique used in machine learning , is a special case of reverse accumulation.
For such problems, to achieve given accuracy, it takes much less computational time to use an implicit method with larger time steps, even taking into account that one needs to solve an equation of the form (1) at each time step. That said, whether one should use an explicit or implicit method depends upon the problem to be solved.