Parallel Iterative Schemes of Linear Algebra with Application to the Stability Analysis of Solutions of Systems of Linear Differential Equations

被引：1
作者：
Ya. E. Romm
机构：
[1] State Pedagogical Institute,
来源：
Cybernetics and Systems Analysis | 2004年 / 40卷 / 4期
关键词：
parallel algorithm; time complexity; linear algebra; linear differential equation; stability;
D O I：
10.1023/B:CASA.0000047878.21086.e9
中图分类号：
学科分类号：
摘要：
Parallel modifications of linear iteration schemes are proposed that are used to solve systems of liner algebraic equations and to achieve the time complexity equal to T = log2k · O(log2n), where k is the number of iterations of an original scheme and n is the dimension of a system. Such schemes are extended to the case of approximate solution of systems of linear differential equations with constant coefficients. Based on them and using a program, the stability of solutions in the Lyapunov sense is analyzed.
引用
收藏
页码：565 / 586
页数：21
相关论文
共 27 条
  • [1] Strassen V.(1969)Gaussian elimination is not optimal Numer. Math. 13 354-356
  • [2] Bini D.(1979)On O (n2.7799) complexity for n n approximate matrix multiplication Inform. Proc. Lett. 8 234-235
  • [3] Capovani M.(1982)Upper estimates of complexity of solving systems of linear equations Theory of Complexity of Computations. I, Proceedings of Scientific Seminars, LOMI of Acad. of Sci. of the USSR 118 159-187
  • [4] Romani F.(1977)Parallel computations in linear algebra. I Kibernetika 6 28-40
  • [5] Lotti G.(1982)Parallel computations in linear algebra. II Kibernetika 3 18-31
  • [6] Solodovnikov V. I.(1980)Conditions of termination of iterative processes that guarantee a specified accuracy Dokl. AN UkrSSR, Ser. A 6 21-23
  • [7] Faddeyeva V. N.(1982)Speedup of linear stationary iteration processes in multiprocessor computers. I Kibernetika 1 47-54
  • [8] Faddeyev D. K.(1982)Acceleration of linear stationary iterative processes in multiprocessor computers. II Kibernetika 3 64-67
  • [9] Faddeyeva V. N.(1995)Efficient algorithms for solution of problems of linear algebra over a field consisting of two elements Review of Applied and Industrial Mathematics 2 399-439
  • [10] Faddeyev D. K.(1988)Machine error of parallel algorithms Kibernetika 2 19-26
123