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

DOI10.1016/0020-0190(80)90045-9zbMath0509.68032OpenAlexW2013785943MaRDI QIDQ1838293

Alberto Pettorossi

Publication date: 1980

Published in: Information Processing Letters (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0020-0190(80)90045-9

zbMATH Keywords

Fibonacci numberslinear recurrence relationsmatrix multiplicationiterative and recursive algorithm

Mathematics Subject Classification ID

Analysis of algorithms and problem complexity (68Q25) Recurrences (11B37)

Related Items (7)

A fast algorithm for computing large Fibonacci numbers ⋮ A Formal Derivation of an 0(log n) Algorithm for Computing Fibonacci Numbers ⋮ Horner's rule and the computation of linear recurrences ⋮ 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 ⋮ On the computing of the generalized order-\(k\) Pell numbers in log time ⋮ Computing sums of order-k Fibonacci numbers in log time

Cites Work

• Unnamed Item
• An O(log n) algorithm for computing general order-k Fibonacci numbers
• Deriving very efficient algorithms for evaluating linear recurrence relations using the program transformation technique
• A Transformation System for Developing Recursive Programs

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