Abstract: By using the actual different hierarchical levels of memory and computational units in parallel architectures, this paper proposes a multilevel parallel algorithm to solve a structured linear system with a symmetric Toeplitz matrix. By means of the appropriate mathematical derivation, a symmetric Toeplitz linear system is translated to a Caucky-like linear system. The algorithm is realized by Message Passing Interface(MPI) and Open Multi-platform shared-memory parallel Programming(OpenMP). Experimental results verify its feasibility.

Key words: Toeplitz matrix, Cauchy-like matrix, multilevel parallel programming, Message Passing Interface(MPI), Open Multi-platform shared-memory parallel Programming(OpenMP)

摘要： 利用并行体系结构中不同层次级别的内存和计算单元，提出一种求解对称结构化特普利茨线性系统的多级并行算法。通过数学推导将特普利茨线性系统转换成柯西式线性系统，利用消息传递接口和开放多平台共享内存并行程序设计工具实现该算法，并通过实验验证其可行性。

关键词: 特普利茨矩阵, 柯西式矩阵, 多级并行程序设计, 消息传递接口, 开放多平台共享内存并行程序设计

CLC Number: 

• TP301.6