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Visualisation of the 3rd to 50th terms of the Kolakoski sequence as a spiral. The terms start at the dot at the middle of the spiral. In the following revolution, each arc is repeated if the term is 1, or divided into two equal halves if it is 2. The first two terms cannot be shown as they are self-referential.
In mathematics, a recurrence relation is an equation according to which the th term of a sequence of numbers is equal to some combination of the previous terms. Often, only previous terms of the sequence appear in the equation, for a parameter that is independent of ; this number is called the order of the relation.
Muller's method is a root-finding algorithm, a numerical method for solving equations of the form f(x) = 0.It was first presented by David E. Muller in 1956.. Muller's method proceeds according to a third-order recurrence relation similar to the second-order recurrence relation of the secant method.
This form may be used with any m, but only works well for m with many repeated prime factors, such as a power of 2; using a computer's word size is the most common choice. If m were a square-free integer , this would only allow a ≡ 1 (mod m ), which makes a very poor PRNG; a selection of possible full-period multipliers is only available when ...
In computer science, cycle detection or cycle finding is the algorithmic problem of finding a cycle in a sequence of iterated function values. For any function f that maps a finite set S to itself, and any initial value x 0 in S , the sequence of iterated function values
A (1, 1) = Trapezoidal (f, tStart, tEnd, h, y0) % Each row of the matrix requires one call to Trapezoidal % This loops starts by filling the second row of the matrix, % since the first row was computed above for i = 1: maxRows-1 % Starting at i = 1, iterate at most maxRows - 1 times % Halve the previous value of h since this is the start of a ...
In multivariable calculus, an iterated limit is a limit of a sequence or a limit of a function in the form , = (,), (,) = ((,)),or other similar forms. An iterated limit is only defined for an expression whose value depends on at least two variables. To evaluate such a limit, one takes the limiting process as one of the two variables approaches some number, getting an expression whose value ...
Furthermore, the mean value of the series can be calculated via: /: ¯ = +. The formula is essentially the same as the formula for the mean of a discrete uniform distribution, interpreting the arithmetic progression as a set of equally probable outcomes.