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  2. Recurrence relation - Wikipedia

    en.wikipedia.org/wiki/Recurrence_relation

    A famous example is the recurrence for the Fibonacci numbers, = + where the order is two and the linear function merely adds the two previous terms. This example is a linear recurrence with constant coefficients , because the coefficients of the linear function (1 and 1) are constants that do not depend on n . {\displaystyle n.}

  3. Linear recurrence with constant coefficients - Wikipedia

    en.wikipedia.org/wiki/Linear_recurrence_with...

    A linear recurrence denotes the evolution of some variable over time, with the current time period or discrete moment in time denoted as t, one period earlier denoted as t − 1, one period later as t + 1, etc. The solution of such an equation is a function of t, and not of any iterate values, giving the value of the iterate at any time.

  4. Recursion - Wikipedia

    en.wikipedia.org/wiki/Recursion

    Recurrence relations are equations which define one or more sequences recursively. Some specific kinds of recurrence relation can be "solved" to obtain a non-recursive definition (e.g., a closed-form expression). Use of recursion in an algorithm has both advantages and disadvantages. The main advantage is usually the simplicity of instructions.

  5. Three-term recurrence relation - Wikipedia

    en.wikipedia.org/wiki/Three-term_recurrence_relation

    If the {} and {} are constant and independent of the step index n, then the TTRR is a Linear recurrence with constant coefficients of order 2. Arguably the simplest, and most prominent, example for this case is the Fibonacci sequence , which has constant coefficients a n = b n = 1 {\displaystyle a_{n}=b_{n}=1} .

  6. Constant-recursive sequence - Wikipedia

    en.wikipedia.org/wiki/Constant-recursive_sequence

    The order of the sequence is the smallest positive integer such that the sequence satisfies a recurrence of order d, or = for the everywhere-zero sequence. [ citation needed ] The definition above allows eventually- periodic sequences such as 1 , 0 , 0 , 0 , … {\displaystyle 1,0,0,0,\ldots } and 0 , 1 , 0 , 0 , … {\displaystyle 0,1,0,0 ...

  7. Lucas sequence - Wikipedia

    en.wikipedia.org/wiki/Lucas_sequence

    LUC is a public-key cryptosystem based on Lucas sequences [5] that implements the analogs of ElGamal (LUCELG), Diffie–Hellman (LUCDIF), and RSA (LUCRSA). The encryption of the message in LUC is computed as a term of certain Lucas sequence, instead of using modular exponentiation as in RSA or Diffie–Hellman.

  8. Clenshaw algorithm - Wikipedia

    en.wikipedia.org/wiki/Clenshaw_algorithm

    The recurrence relation for ⁡ is ⁡ (+) = ⁡ ⁡ ⁡ (), making the coefficients in the recursion relation = ⁡, = and the evaluation of the series is given by + = + =, = + ⁡ + + (), The final step is made particularly simple because () = ⁡ =, so the end of the recurrence is simply () ⁡ (); the term is added separately: = + ⁡.

  9. Master theorem (analysis of algorithms) - Wikipedia

    en.wikipedia.org/wiki/Master_theorem_(analysis...

    The master theorem always yields asymptotically tight bounds to recurrences from divide and conquer algorithms that partition an input into smaller subproblems of equal sizes, solve the subproblems recursively, and then combine the subproblem solutions to give a solution to the original problem.