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In computing, the utility diff is a data comparison tool that computes and displays the differences between the contents of files. Unlike edit distance notions used for other purposes, diff is line-oriented rather than character-oriented, but it is like Levenshtein distance in that it tries to determine the smallest set of deletions and insertions to create one file from the other.
In an analogous way, one can obtain finite difference approximations to higher order derivatives and differential operators. For example, by using the above central difference formula for f ′(x + h / 2 ) and f ′(x − h / 2 ) and applying a central difference formula for the derivative of f ′ at x, we obtain the central difference approximation of the second derivative of f:
The finite difference method relies on discretizing a function on a grid. 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).
In information theory, linguistics, and computer science, the Levenshtein distance is a string metric for measuring the difference between two sequences. The Levenshtein distance between two words is the minimum number of single-character edits (insertions, deletions or substitutions) required to change one word into the other.
The classical finite-difference approximations for numerical differentiation are ill-conditioned. However, if is a holomorphic function, real-valued on the real line, which can be evaluated at points in the complex plane near , then there are stable methods.
The weave-diff can compare paragraphs word-for-word if moved, but not if split. A diff shows differences per line, so it synchronizes between revisions by matching the newlines and unchanged lines. Some editors find that having additional line breaks to break up the text improves the diff function.
Displaying the differences between two or more sets of data, file comparison tools can make computing simpler, and more efficient by focusing on new data and ignoring what did not change. Generically known as a diff [1] after the Unix diff utility, there are a range of ways to compare data sources and display the results.
Which of these two types should be used depends on the sweep count. The computational complexity of one sweep is proportional to the complexity of the original code. Forward accumulation is more efficient than reverse accumulation for functions f : R n → R m with n ≪ m as only n sweeps are necessary, compared to m sweeps for reverse ...