Parallel algorithms for solving certain classes of linear recurrences
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 Xi=aiXi−1+di for 1≤i≤n in 210gn units of time using only 3/4n processors. The second results relate to solving Xi=Xi−1+Xi−2+di for 1≤i≤n. It is shown that Xi's can be computed in at most 310gn units of time using 5/4n processors. In the special case when di=0 for all i, it is shown that Xi'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.
KeywordsParallel Algorithm Fibonacci Number Linear Recurrence Cyclic Reduction Tridiagonal Linear System
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