# Parallel algorithms for solving certain classes of linear recurrences

## Abstract

This paper presents two new time and/or processor bounds for solving certain classes of linear recurrences. The first result provides a parallel algorithm for solving X_{i}=a_{i}X_{i−1}+d_{i} for 1≤i≤n in 210gn units of time using only 3/4n processors. The second results relate to solving X_{i}=X_{i−1}+X_{i−2}+d_{i} for 1≤i≤n. It is shown that X_{i}'s can be computed in at most 310gn units of time using 5/4n processors. In the special case when d_{i}=0 for all i, it is shown that X_{i}'s (the first n-Fibonacci numbers) can be computed in parallel in 210gn-1 units of time using only n/2 processors. These time and processor bounds compare very favourably with the previously known results for these problems.

## Keywords

Parallel Algorithm Fibonacci Number Linear Recurrence Cyclic Reduction Tridiagonal Linear System## Preview

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