Titlebook: A History of Algorithms; From the Pebble to t Jean-Luc Chabert Book 1999 Springer-Verlag Berlin Heidelberg 1999 Approximation.Bézout‘s iden

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Algorithms for Computational Biologyquare cells contain numbers such that the sum of the numbers along any row, column or diagonal produces the same result. A magic square containing . rows and . columns is called an order . magic square. Mathematically, it is often useful to consider the square as a particular . possessing the .. whi

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K. O. Geddes,S. R. Czapor,G. Labahn procedure, and that it has relevance right up to today. It can be of use, not only in the search for the greatest common divisor, as described by Euclid himself (Section 4.1), but also, by adapting the procedure, in the solution of indeterminate equations, leading to Bézout’s identity (Section 4.3)

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Witness Lists (Density Theorem),nvergence. It is known, in practice, by two names, depending on the circumstances in which it is used. When finding successive approximations to the numerical solution of an equation: ., it is called the . or simply Newton’s method. When flnding y expressed as a series in x, given an equation: ., it

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Algorithms for Continuous Optimizationin Babylonian and Egyptian mathematics, and also in Indian mathematics of the Middle Ages, as well in Islamic countries and in Europe [.]. It becomes quite difficult however to decide in which branch of mathematics we should place the corresponding algorithms for solving these problems. Their soluti

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Brian Steele,John Chandler,Swarna Reddyns many times. We have seen how tables have been constructed from the earliest times, for example, the Babylonians produced tables for calculating ‘inverses’ (Section 1.2 above). In Astronomy, trigonometric tables have played a major role, and these correspond to the tables of chords that Ptolemy pr

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Brian Steele,John Chandler,Swarna Reddyre of a circle, or ‘squaring the circle’, is the best known example. The meaning of quadrature quickly began to take on an extended meaning of comparing the areas of two plane figures, one of which was already known — for example, a figure bounded by straight lines. Thus quadrature came to mean esta

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Brian Steele,John Chandler,Swarna Reddyer differential equations. There followed a systematic study of differential equations in the 18th century, and particularly in the 19th century, as a consequence of applying Newton’s Laws of mechanics to determine the trajectories of celestial bodies, since the study of a mechanical system of . ‘ma

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Brian Steele,John Chandler,Swarna Reddyg a clear distinction between two points of view. In principle, with interpolation, we construct a function which has to take specific values for a finite number of values of the variable, whereas, with approximating, we look for a function which approximates ‘as well as possible’ the values of the