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The tablet also gives an example where one side of the square is 30, and the resulting diagonal is 42 25 35 or 42.4263888. Computational mathematics is the study of the interaction between mathematics and calculations done by a computer. [1]
A computation is any type of arithmetic or non-arithmetic calculation that is well-defined. [1] [2] Common examples of computation are mathematical equation solving and the execution of computer algorithms. Mechanical or electronic devices (or, historically, people) that perform computations are known as computers.
An example of this type of work is the computation of polynomial greatest common divisors, a task required to simplify fractions and an essential component of computer algebra. Classical algorithms for this computation, such as Euclid's algorithm, proved inefficient over infinite fields; algorithms from linear algebra faced similar struggles. [22]
For example, the computation of polynomial greatest common divisors is systematically used for the simplification of expressions involving fractions. This large amount of required computer capabilities explains the small number of general-purpose computer algebra systems.
In a fraction, the number of equal parts being described is the numerator (from Latin: numerātor, "counter" or "numberer"), and the type or variety of the parts is the denominator (from Latin: dēnōminātor, "thing that names or designates").
The continued fraction method is based on Dixon's factorization method. It uses convergents in the regular continued fraction expansion of , +. Since this is a quadratic irrational, the continued fraction must be periodic (unless n is square, in which case the factorization is obvious).
Another meaning for generalized continued fraction is a generalization to higher dimensions. For example, there is a close relationship between the simple continued fraction in canonical form for the irrational real number α, and the way lattice points in two dimensions lie to either side of the line y = αx. Generalizing this idea, one might ...
The Crank–Nicolson stencil for a 1D problem. In mathematics, especially the areas of numerical analysis concentrating on the numerical solution of partial differential equations, a stencil is a geometric arrangement of a nodal group that relate to the point of interest by using a numerical approximation routine.