A Highly Parallel Systolic Tridiagonal Solver

Takashi NARITOMI; Hirotomo ASO

A Highly Parallel Systolic Tridiagonal Solver

Takashi NARITOMI, Hirotomo ASO

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Many numerical simulation problems of natural phenomena are formulated by large tridiagonal and block tridiagonal linear systems. In this paper, an efficient parallel algorithm to solve a tridiagonal linear system is proposed. The algorithm named bi-recurrence algorithm has an inherent parallelism which is suitable for parallel processing. Its time complexity is 8N - 4 for a tridiagonal linear system of order N. The complexity is little more than the Gaussian elimination algorithm. For parallel implementation with two processors, the time complexity is 4N - 1. Based on the bi-recurrence algorithm, a VLSI oriented tridiagonal solver is designed, which has an architecture of 1-D linear systolic array with three processing cells. The systolic tridiagonal solver completes finding the solution of a tridiagonal linear system in 3N + 6 units of time. A highly parallel systolic tridiagonal solver is also presented. The solver is characterized by highly parallel computability which originates in the divide-and-conquer strategy and high cost performance which originates in the systolic architecture. This solver completes finding the solution in 10(N/p) + 6p + 23 time units, where p is the number of partitions of the system.

Publication: IEICE TRANSACTIONS on Information Vol.E79-D No.9 pp.1241-1247

Publication Date: 1996/09/25

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Category: Computer Systems

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Takashi NARITOMI, Hirotomo ASO, "A Highly Parallel Systolic Tridiagonal Solver" in IEICE TRANSACTIONS on Information, vol. E79-D, no. 9, pp. 1241-1247, September 1996, doi: .
Abstract: Many numerical simulation problems of natural phenomena are formulated by large tridiagonal and block tridiagonal linear systems. In this paper, an efficient parallel algorithm to solve a tridiagonal linear system is proposed. The algorithm named bi-recurrence algorithm has an inherent parallelism which is suitable for parallel processing. Its time complexity is 8N - 4 for a tridiagonal linear system of order N. The complexity is little more than the Gaussian elimination algorithm. For parallel implementation with two processors, the time complexity is 4N - 1. Based on the bi-recurrence algorithm, a VLSI oriented tridiagonal solver is designed, which has an architecture of 1-D linear systolic array with three processing cells. The systolic tridiagonal solver completes finding the solution of a tridiagonal linear system in 3N + 6 units of time. A highly parallel systolic tridiagonal solver is also presented. The solver is characterized by highly parallel computability which originates in the divide-and-conquer strategy and high cost performance which originates in the systolic architecture. This solver completes finding the solution in 10(N/p) + 6p + 23 time units, where p is the number of partitions of the system.
URL: https://global.ieice.org/en_transactions/information/10.1587/e79-d_9_1241/_p

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@ARTICLE{e79-d_9_1241,
author={Takashi NARITOMI, Hirotomo ASO, },
journal={IEICE TRANSACTIONS on Information},
title={A Highly Parallel Systolic Tridiagonal Solver},
year={1996},
volume={E79-D},
number={9},
pages={1241-1247},
abstract={Many numerical simulation problems of natural phenomena are formulated by large tridiagonal and block tridiagonal linear systems. In this paper, an efficient parallel algorithm to solve a tridiagonal linear system is proposed. The algorithm named bi-recurrence algorithm has an inherent parallelism which is suitable for parallel processing. Its time complexity is 8N - 4 for a tridiagonal linear system of order N. The complexity is little more than the Gaussian elimination algorithm. For parallel implementation with two processors, the time complexity is 4N - 1. Based on the bi-recurrence algorithm, a VLSI oriented tridiagonal solver is designed, which has an architecture of 1-D linear systolic array with three processing cells. The systolic tridiagonal solver completes finding the solution of a tridiagonal linear system in 3N + 6 units of time. A highly parallel systolic tridiagonal solver is also presented. The solver is characterized by highly parallel computability which originates in the divide-and-conquer strategy and high cost performance which originates in the systolic architecture. This solver completes finding the solution in 10(N/p) + 6p + 23 time units, where p is the number of partitions of the system.},
keywords={},
doi={},
ISSN={},
month={September},}

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TY - JOUR
TI - A Highly Parallel Systolic Tridiagonal Solver
T2 - IEICE TRANSACTIONS on Information
SP - 1241
EP - 1247
AU - Takashi NARITOMI
AU - Hirotomo ASO
PY - 1996
DO -
JO - IEICE TRANSACTIONS on Information
SN -
VL - E79-D
IS - 9
JA - IEICE TRANSACTIONS on Information
Y1 - September 1996
AB - Many numerical simulation problems of natural phenomena are formulated by large tridiagonal and block tridiagonal linear systems. In this paper, an efficient parallel algorithm to solve a tridiagonal linear system is proposed. The algorithm named bi-recurrence algorithm has an inherent parallelism which is suitable for parallel processing. Its time complexity is 8N - 4 for a tridiagonal linear system of order N. The complexity is little more than the Gaussian elimination algorithm. For parallel implementation with two processors, the time complexity is 4N - 1. Based on the bi-recurrence algorithm, a VLSI oriented tridiagonal solver is designed, which has an architecture of 1-D linear systolic array with three processing cells. The systolic tridiagonal solver completes finding the solution of a tridiagonal linear system in 3N + 6 units of time. A highly parallel systolic tridiagonal solver is also presented. The solver is characterized by highly parallel computability which originates in the divide-and-conquer strategy and high cost performance which originates in the systolic architecture. This solver completes finding the solution in 10(N/p) + 6p + 23 time units, where p is the number of partitions of the system.
ER -