Search results
Results from the WOW.Com Content Network
The Euclidean algorithm was the first integer relation algorithm, which is a method for finding integer relations between commensurate real numbers. Several novel integer relation algorithms have been developed, such as the algorithm of Helaman Ferguson and R.W. Forcade (1979) [ 49 ] and the LLL algorithm .
The Routh array is a tabular method permitting one to establish the stability of a system using only the coefficients of the characteristic polynomial.Central to the field of control systems design, the Routh–Hurwitz theorem and Routh array emerge by using the Euclidean algorithm and Sturm's theorem in evaluating Cauchy indices.
A Euclidean domain is an integral domain which can be endowed with at least one Euclidean function. A particular Euclidean function f is not part of the definition of a Euclidean domain, as, in general, a Euclidean domain may admit many different Euclidean functions. In this context, q and r are called respectively a quotient and a remainder of ...
For this reason, methods have been designed to modify Euclid's algorithm for working only with polynomials over the integers. They consist of replacing the Euclidean division, which introduces fractions, by a so-called pseudo-division, and replacing the remainder sequence of the Euclid's algorithm by so-called pseudo-remainder sequences (see ...
Euclidean domains (also known as Euclidean rings) [7] are defined as integral domains which support the following generalization of Euclidean division: Given an element a and a non-zero element b in a Euclidean domain R equipped with a Euclidean function d (also known as a Euclidean valuation [ 8 ] or degree function [ 7 ] ), there exist q and ...
The binary GCD algorithm, also known as Stein's algorithm or the binary Euclidean algorithm, [1] [2] is an algorithm that computes the greatest common divisor (GCD) of two nonnegative integers. Stein's algorithm uses simpler arithmetic operations than the conventional Euclidean algorithm ; it replaces division with arithmetic shifts ...
Harmonic analysis is a branch of mathematics concerned with investigating the connections between a function and its representation in frequency.The frequency representation is found by using the Fourier transform for functions on unbounded domains such as the full real line or by Fourier series for functions on bounded domains, especially periodic functions on finite intervals.
Isomap is used for computing a quasi-isometric, low-dimensional embedding of a set of high-dimensional data points. The algorithm provides a simple method for estimating the intrinsic geometry of a data manifold based on a rough estimate of each data point’s neighbors on the manifold. Isomap is highly efficient and generally applicable to a ...