Distributed​ Systems Assignment 6 Solution

In this Assignment, you will write parallel codes using mpi

(100 marks)

programming for solving Linear Systems. You can refer to Chapter

12 of the book (Parallel Programming in C with MPI and OpenMP by

Micheal J. quinn, 2003) for more details on the topic and algorithms.

Language Constraint: ​C/C++

Include a bash script to run each of the code in your submission.

Name them q1.sh, q2.sh

Marks for each question are for code + explanation.

Q 1)

(40 marks)

Implement a parallel program to solve a system of linear equations

Ax = b using the ​Gaussian Elimination row-oriented algorithm

followed by back substitution. Your program should input the system

of equations from a file. The file contains a matrix of doubles, the first

two elements of the file are two integers. The first has the value n,

the second has the value n + 1. The remainder of the file contains

n(n + 1) doubles, corresponding to the elements of A and b stored in

this order:

Q 2)

(40 marks)

Implement a parallel program to solve a system of linear equations

Ax = b using the ​Conjugate Gradient Method​. You can be assured

that A is a symmetric, positive definite matrix.

Your program should input the system of equations from a file. The

file contains a matrix of doubles. The first two elements of the file are

two integers. The first has the value n,the second has the value n +1.

The remainder of the file contains n(n + 1) doubles, corresponding to

the elements of A and b stored in this order

Q 3)

(20 marks)

Prepare a Readme showing Comparison of the performance of these

two algorithms and show the results. You have to generate input for

performance comparison. (Take matrix A of considerable size, say

1000X1000)