# Gaussian elimination with partial pivoting and load balancing on a multiprocessor

## Abstract

A row-oriented implementation of Gaussian elimination with partial pivoting on a local-memory multiprocessor is described. In the absence of pivoting, the initial data loading of the node processors leads to a balanced computation. However, if interchanges occur, the computational loads on the processors may become unbalanced, leading to inefficiency. A simple load balancing scheme is described which is inexpensive and which maintains computational balance in the presence of pivoting. Using some reasonable assumptions about the probability of pivoting occurring, an analysis of the communication costs of the algorithm is developed, along with an analysis of the computation performed in each node processor. This model is then used to derive the expected speed-up of the algorithm. Finally, experiments using an Intel iPSC hypercube are presented in order to demonstrate the extent to which the analytical model predicts the performance. 11 refs., 2 tabs.

- Authors:

- Publication Date:

- Research Org.:
- Oak Ridge National Lab., TN (USA)

- OSTI Identifier:
- 6636181

- Report Number(s):
- ORNL/TM-10323

ON: DE87007784

- DOE Contract Number:
- AC05-84OR21400

- Resource Type:
- Technical Report

- Resource Relation:
- Other Information: Portions of this document are illegible in microfiche products. Original copy available until stock is exhausted

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 99 GENERAL AND MISCELLANEOUS//MATHEMATICS, COMPUTING, AND INFORMATION SCIENCE; ARRAY PROCESSORS; TASK SCHEDULING; ALGORITHMS; PERFORMANCE TESTING; DATA PROCESSING; MATHEMATICAL LOGIC; PROCESSING; TESTING; 990210* - Supercomputers- (1987-1989)

### Citation Formats

```
George, A., and Chu, E.
```*Gaussian elimination with partial pivoting and load balancing on a multiprocessor*. United States: N. p., 1987.
Web. doi:10.2172/6636181.

```
George, A., & Chu, E.
```*Gaussian elimination with partial pivoting and load balancing on a multiprocessor*. United States. https://doi.org/10.2172/6636181

```
George, A., and Chu, E. Sun .
"Gaussian elimination with partial pivoting and load balancing on a multiprocessor". United States. https://doi.org/10.2172/6636181. https://www.osti.gov/servlets/purl/6636181.
```

```
@article{osti_6636181,
```

title = {Gaussian elimination with partial pivoting and load balancing on a multiprocessor},

author = {George, A. and Chu, E.},

abstractNote = {A row-oriented implementation of Gaussian elimination with partial pivoting on a local-memory multiprocessor is described. In the absence of pivoting, the initial data loading of the node processors leads to a balanced computation. However, if interchanges occur, the computational loads on the processors may become unbalanced, leading to inefficiency. A simple load balancing scheme is described which is inexpensive and which maintains computational balance in the presence of pivoting. Using some reasonable assumptions about the probability of pivoting occurring, an analysis of the communication costs of the algorithm is developed, along with an analysis of the computation performed in each node processor. This model is then used to derive the expected speed-up of the algorithm. Finally, experiments using an Intel iPSC hypercube are presented in order to demonstrate the extent to which the analytical model predicts the performance. 11 refs., 2 tabs.},

doi = {10.2172/6636181},

url = {https://www.osti.gov/biblio/6636181},
journal = {},

number = ,

volume = ,

place = {United States},

year = {1987},

month = {3}

}