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Top1. Introduction
The current drift of technology as predicted by Moore was of inducing more number of semiconductors on a smaller chip. This has change the face of technology increased the computational power of even a small hand held device. But it was perceived that only the hardware evolution was not adequate enough. The software also needed to make leap in a way to complement the upgraded hardware configuration. This lead to the concept of concurrent execution of programs on shared memory system with more than one processors (cores).
The effect of the changing architecture can be very well be seen on the problems that are of the category of dense linear algebra such as the Linear Equation solving. These problems expect one of the two solutions as given below.
There are many existing methods available to solve Linear Equations; listed below.
The above said methods give a better speedup; but when implemented concurrently; it will not reach to the expected speedup.
Some factors which affect the speed up of parallelization are mentioned below.
Dense linear algebraic equations are implemented in parallel using GPU based systems, the load balancing methods and it also uses the static and dynamic paradigms of available parallelization libraries.
These methods are not as efficient and the increasing expectations won’t be fulfilled by them. The solution to this dilemma exists in the ancient Indian scriptures. The ancient Indian scriptures mainly the Atharvaveda’s sub-section (Upveda) named “Sthapathyaveda” it contains account of all the engineering and architecture related works. These scriptures also consist various different method to deal with linear equations that are very aptly decrypted by Sri Krsna Tirthaji Maharaj (Tirthji, Sri Bharti Krsna (Bankagarya of Oovardhana Matha, 1981). These methods are way better than the conventional methods. The methods available for solving linear equations in Vedic mathematics are listed below.
But the biggest question that surfaced was will these methods be able to adapt the parallelization? Will the method be able to deliver the immense performance of sequential implementation even in the parallelized form?
The rest of the article will contain the following aspects of the work; section two consist the related work and comparative analysis of the conventional method and Vedic method. Section three will contain the analysis of the parallelizability of Paravartya Yojayet and LU Factorization. Section four will highlight Factors that could affected the time complexity of the parallel implementation. Section five will contain a detailed analysis of the Results along with the discussions. Section six will be concluding remarks for the work and the section seven the future scope of the work.