Abstract:
Systemsoflinearequationsareusedinavarietyoffields. Thecanonicalproblemofsolving 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 approachallowsforadistributedmessage-passingimplementationofthesolutionalgorithm. 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.
