• 论文 •

### 关于线性递推问题的并行算法

1. 应用物理与计算数学研究所
• 出版日期:1988-02-20 发布日期:1988-02-20

### PARALLEL ALGORITHMS ON LINEAR RECURRENCE PROBLEMS

1. Zhang Bao-lin Institute of Applied Physics and Computational Mathematics
• Online:1988-02-20 Published:1988-02-20

This paper gives a general idea and the algorithms for solving linear recurrenceproblems on parallel computers. The parallel algorithms and their time complexityto the first-order linear recurrence problem, the second-order and Mth-order linearhomogeneous recurrence problems are investigated. Take the second-order problem:findingx_i=a_ix_(i-1)+b_ix_(i-2), i=1, 2, …, nwhere a_i, b_i are constants, x_0, x_(-1) are given initial values, k<i_0,x_i=A_(i,1)~(i_0)x_(i_0)+A_(i,2)~(i_0)x_(i_0-1)in which A_(i,1)~(i_0) and A_(i,2)~(i_0) are_i_2 constants depending on i_0. Futhermore, A_(i,1)~(i_0) and A_(i,2)~(i_0) canrespectively be computed by choosing x_(i_0)=1, x_(i_0-1)=0 and x_(i_0)=0, x_(i_O-1)=1, asfollows:x_k=a_kx_(k-1)+b_kx_(k-2)k=i_0+1, i_0+2, …, i. The speedup of algorithm PLA2 is about k/3, betterthan that of the well known matrix method.
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