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Thus, a representation that compresses the storage size of a file from 10 MB to 2 MB yields a space saving of 1 - 2/10 = 0.8, often notated as a percentage, 80%. For signals of indefinite size, such as streaming audio and video, the compression ratio is defined in terms of uncompressed and compressed data rates instead of data sizes:
the data may be encoded as "279 red pixels". This is a basic example of run-length encoding; there are many schemes to reduce file size by eliminating redundancy. The Lempel–Ziv (LZ) compression methods are among the most popular algorithms for lossless storage. [6]
Allows the user to adjust the balance between compression ratio and compression speed, without affecting the speed of decompression; LZO supports overlapping compression and in-place decompression. As a block compression algorithm, it compresses and decompresses blocks of data. Block size must be the same for compression and decompression.
In numerical analysis, the Bulirsch–Stoer algorithm is a method for the numerical solution of ordinary differential equations which combines three powerful ideas: Richardson extrapolation, the use of rational function extrapolation in Richardson-type applications, and the modified midpoint method, [1] to obtain numerical solutions to ordinary ...
The "trick" that allows lossless compression algorithms, used on the type of data they were designed for, to consistently compress such files to a shorter form is that the files the algorithms are designed to act on all have some form of easily modeled redundancy that the algorithm is designed to remove, and thus belong to the subset of files ...
As an example consider the sequence of tokens AABBA which would assemble the dictionary; 0 {0,_} 1 {0,A} 2 {1,B} 3 {0,B} and the output sequence of the compressed data would be 0A1B0B. Note that the last A is not represented yet as the algorithm cannot know what comes next. In practice an EOF marker is added to the input – AABBA$ for
LZW compression became the first widely used universal data compression method on computers. A large English text file can typically be compressed via LZW to about half its original size. LZW was used in the public-domain program compress , which became a more or less standard utility in Unix systems around 1986.
Even binary data files can be compressed with this method; file format specifications often dictate repeated bytes in files as padding space. However, newer compression methods such as DEFLATE often use LZ77-based algorithms, a generalization of run-length encoding that can take advantage of runs of strings of characters (such as BWWBWWBWWBWW).