Complexity Analysis of Vedic Mathematics Algorithms for Multicore Environment

Abstract

The huge computations performed sequentially requires a lot of time for execution as on contrary to the concurrent implementation. Many problems are involved in the dense linear algebra operations the main focus for this work is for solving linear equations. The problem of solving linear equations when approached using parallel implementation will yield better results. The Vedic mathematical method of Paravartya Yojayet is having less complexity as compared to the conventional methods. This work mainly focuses on the parallel implementation of the Paravartya Yojayet and its comparison to the benchmarking of the existing LU decomposition. The results of this implementation of Paravartya Yojayet are better when analysed theoretically but its actual parallel implementation will vary so it needs to be analysed and this work presents the same. The comparative analysis of the two ways for parallelization of the Paravartya Yojayet methods viz. ‘For loop' parallelization and the ‘direct parallelization' is also analysed in this work.

Vedic Mathematics Approach to Speedup Parallel Computations

“…The analysis of Sankalana Vyavakalanabhyam method iv. The analysis of Sopantyadvayamantyam method Vedic mathematics is an ancient most mathematical catalogue of various approaches [8], [9], [10] to solve any numerical computation. Vedic mathematics is said to be descended from the Atharva Veda's Upaveda (sub section) named Sthapathyaveda that contains all the records of the engineering technology and computational strategies.…”

“…Hence the need arises for the use of Vedic mathematical principles that satisfy void left by conventional mathematics. Vedic mathematics is acclaimed for yielding accurate results in minimum time [8], [9], [10]. These mathematical principles involve the use of simple arithmetic operations to compute a very large problem in most efficient manner.…”

Analysis of Factors of Parallelism and their Impact on Dense Algebra Problems

“…This has to be done before the cores are allocated to the underlying threads for execution. Even if the system has multi-processor systems capable of processing multiple sub tasks at a time, extreme parallelization cannot be achieved because of the synchronization and connectivity issues [16]. Since the ultimate goal of computing is to speed up the processing, parallelization without more overheads [17] it becoming a hurdle, will need to be controlled and managed.…”