Abstract:
Systems of linear equations are used in a variety of fields. The canonical problem of solving
a system of linear equations arises in numerous contexts in information theory, communication
theory, and related fields. This thesis 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 for different dimension
size n of system of linear equation . At the end, a graph can be plotted with time
taken for execution of a method considered V/s dimension size n. In this contribution, we
develop a solution that does not involve direct matrix inversion. The iterative nature of our
approach allows for a distributed message-passing implementation of the solution algorithm.
We present test results which show that our solver achieves good results, both in terms of
numerical accuracy as well as computing time. Furthermore, even very large systems (n
1000) can be solved given a cluster with sufficient resources. We also address some properties
of the algorithm, including convergence, exactness, its complexity order and relation to
classical solution methods.
Description:
We are thankful to Almighty Allah for his blessings for the successful completion of our
thesis. Our heartiest gratitude, profound indebtedness and deep respect go to our supervisor
Dr. M. Kaykobad, Professor, Department of CSE, BUET, Dhaka, Bangladesh, for his
constant supervision, affectionate guidance and great encouragement and motivation. His
keen interest on the topic and valuable advices throughout the study was of great help in
completing thesis.
We are especially grateful to the Department of Computer Science and Engineering (CSE)
of Military Institute of Science and Technology (MIST) for providing their all out support
during the thesis work.
Finally, we would like to thank our families and our course mates for their appreciable
assistance, patience and suggestions during the course of our thesis.
Dhaka Jannatul Maowa
December 2012 Sraboni Kabir
. Ibn Md. Abu Saleh Khosru
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