Projects

Solving system of linear equations using parallel processing

 

Title of the project

 

Solving system of linear equations using parallel processing

 

Abstract of the project

 

This project is aimed at analyzing the available methods for solving a system of linear equations of the form n x n. Using a couple of iterative and/or direct methods, implement a program for these methods that could be run on a parallel processor. At the end, a graph can be plotted with time taken for execution of a method considered V/s number of processors used (2, 4, 8, 32). For example following questions need to be addressed –

  1. For a method considered, evaluate that as the number of processors is increased does the time taken necessarily reduce to solve the equation(s).
  2. For a given number of processors which is the best method that could be employed which takes least time.

 

Keywords

 

Generic Technology keywords

 

Parallel Processing, Linear equation methods

 

Specific Technology keywords

 

Unix/ Windows,C

 

Project type keywords

 

Analysis, Implementation

 

Functional components of the project

 

  1. Parallel processing engine implementation
  2. Implementation of algorithms to solve system of linear equations of the form Ax=B (matrix size NxN) using the parallel processing engine.

 

Steps to start-off the project

 

  1. Understanding of Parallel Processing technology
  2. Study of methods available to solve a system of linear equation of the form Ax=b (matrix size of NxN)

 

Requirements

 

Hardware requirements

 

Number

Description

Alternatives (If available)

1

Windows

UNIX

 

 

 

 

Software requirements

Number

Description

Alternatives (If available)

1

C

C++

2

gcc compiler

 

 

Manpower requirements

 

3-4 people over a period of 6 months

 

Milestones and Timelines

 

Number

Milestone Name

Milestone Description

 

 

Timeline

 

Duration in months

Remarks

 

The weightage of this milestone in percentage of the total project

1

Parallel processing technology and solving linear equations methods

Key methods considered

1 month

25%

2

Programming each method and evaluating on a single processor to start with and then can be extended to muti-processor environment

Code written should make use of least processor cycles.

4 months

50%

3

Calculating the time taken to solve each method for a nxn matrix

Plotting of graph of timetaken for a method considered v/s number of processors used

1 month

20%

 

 

 

 

 

 

 

Guidelines and References

 

  1. Parallel processing documents as available in the Internet

 

  1. Methods available that could be implemented for parallel processors. Ex: Jacobi, Gauss-Seidel, Direct etc


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