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In mathematics and computer science, Recamán's sequence [1] [2] is a well known sequence defined by a recurrence relation. Because its elements are related to the previous elements in a straightforward way, they are often defined using recursion.
Levinson recursion or Levinson–Durbin recursion is a procedure in linear algebra to recursively calculate the solution to an equation involving a Toeplitz matrix. The algorithm runs in Θ ( n 2 ) time, which is a strong improvement over Gauss–Jordan elimination , which runs in Θ( n 3 ).
The maximum period of the two LCGs used is calculated using the formula: [1] This equates to 2.1×10 9 for the two LCGs used. This CLCG shown in this example has a maximum period of: ( m 1 − 1 ) ( m 2 − 1 ) / 2 ≈ 2.3 × 10 18 {\displaystyle (m_{1}-1)(m_{2}-1)/2\approx 2.3\times 10^{18}} This represents a tremendous improvement over the ...
A classic example of recursion is computing the factorial, which is defined recursively by 0! := 1 and n! := n × (n - 1)!.. To recursively compute its result on a given input, a recursive function calls (a copy of) itself with a different ("smaller" in some way) input and uses the result of this call to construct its result.
In mathematics and computer science, mutual recursion is a form of recursion where two mathematical or computational objects, such as functions or datatypes, are defined in terms of each other. [1] Mutual recursion is very common in functional programming and in some problem domains, such as recursive descent parsers , where the datatypes are ...
Thus the first reduction step produces a value at most m + a − 1 ≤ 2m − 2 = 2 e+1 − 4. This is an ( e + 1)-bit number, which can be greater than m (i.e. might have bit e set), but the high half is at most 1, and if it is, the low e bits will be strictly less than m .
Notable examples of systems employing polymorphic recursion include Dussart, Henglein and Mossin's binding-time analysis [2] and the Tofte–Talpin region-based memory management system. [3] As these systems assume the expressions have already been typed in an underlying type system (not necessary employing polymorphic recursion), inference can ...
The algorithm is numerically stable [1] when compared to direct evaluation of polynomials. The computational complexity of this algorithm is (), where d is the number of dimensions, and n is the number of control points. There exist faster alternatives. [2] [3]