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In computer science, a generator is a routine that can be used to control the iteration behaviour of a loop.All generators are also iterators. [1] A generator is very similar to a function that returns an array, in that a generator has parameters, can be called, and generates a sequence of values.
An example where convolutions of generating functions are useful allows us to solve for a specific closed-form function representing the ordinary generating function for the Catalan numbers, C n. In particular, this sequence has the combinatorial interpretation as being the number of ways to insert parentheses into the product x 0 · x 1 ·⋯ ...
Unfortunately, most programming languages make the latter much easier to write (X % r), so it is very commonly used. The generator is not sensitive to the choice of c, as long as it is relatively prime to the modulus (e.g. if m is a power of 2, then c must be odd), so the value c=1 is commonly chosen.
Moreover, since the single factorial function is given by both ! = (,) and ! = (,), we can generate the single factorial function terms using the approximate rational convergent generating functions up to order . This observation suggests an approach to approximating the exact (formal) Laplace–Borel transform usually given in terms of the ...
The generating function F for this transformation is of the third kind, = (,). To find F explicitly, use the equation for its derivative from the table above, =, and substitute the expression for P from equation , expressed in terms of p and Q:
Fitting of a noisy curve by an asymmetrical peak model, with an iterative process (Gauss–Newton algorithm with variable damping factor α).Curve fitting [1] [2] is the process of constructing a curve, or mathematical function, that has the best fit to a series of data points, [3] possibly subject to constraints.
KCachegrind : powerful tool to generate and analyze call graphs based on data generated by callgrind; Mac OS X Activity Monitor : Apple GUI process monitor Activity Monitor has a built-in call graph generator that can sample processes and return a call graph. This function is only available in Mac OS X Leopard
The original use of interpolation polynomials was to approximate values of important transcendental functions such as natural logarithm and trigonometric functions.Starting with a few accurately computed data points, the corresponding interpolation polynomial will approximate the function at an arbitrary nearby point.