Abstract: Publisher SummaryThis chapter presents a discussion on Euclidean fugues. This discussion includes the algorithm of Euclid, Euclidean ring, and the extended Euclidean algorithm. The algorithm of Euclid is best known as an algorithm to compute a greatest common divisor of two integers or two polynomials, but it can as well be used to compute a greatest common divisor of two elements from a general Euclidean domain. This is commonly defined as an integral domain where a certain division property holds that forms the basis of the Euclidean algorithm. The Euclidean algorithm tracks the signal as it penetrates in the layered medium. The extended Euclidean algorithm uses a layer peeling technique to compute the effect of the successive layers (compute Vk) and uses this information to build up the model (multiply out V0,k). However, this is not what is usually meant by a layer adjoining algorithm. In contrast to the layer peeling method, where the effect of the first layer is computed for the whole signal, the layer adjoining method will only process as much of the signal as is needed to identify the first layer.
Publication Year: 1997
Publication Date: 1997-01-01
Language: en
Type: book-chapter
Indexed In: ['crossref']
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