A Formal Derivation of an 0(log n) Algorithm for Computing Fibonacci Numbers

DOI10.1080/02522667.1986.10698833zbMath0587.10001OpenAlexW2061813384MaRDI QIDQ3714128

M. C. Er

Publication date: 1986

Published in: Journal of Information and Optimization Sciences (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/02522667.1986.10698833

zbMATH Keywords

Fibonacci numbersrecursive algorithmcomputational number theoryDijkstra's methodology

Mathematics Subject Classification ID

Software, source code, etc. for problems pertaining to number theory (11-04) Fibonacci and Lucas numbers and polynomials and generalizations (11B39) Calculation of integer sequences (11Y55)

Related Items (2)

An O(k²log(n/k)) Algorithm for Computing Generalized Order-k Fibonacci Numbers with Linear Space ⋮ Fast computation of solutions of linear difference equations by Er's rule

Cites Work

• A presentation of the Fibonacci algorithm
• An O(log n) algorithm for computing general order-k Fibonacci numbers
• Computing Fibonacci numbers (and similarly defined functions) in log time
• An \(O(\log n)\) algorithm for computing the \(n\)th element of the solution of a difference equation
• An interative program to calculate Fibonacci numbers in O(log n) arithmetic operations
• Derivation of an \(O(k^ 2\log n)\) algorithm for computing order-k Fibonacci numbers from the \(O(k^ 3\log n)\) matrix multiplication method
• A Fast Algorithm for Computing Order-K Fibonacci Numbers
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