Efficient approach for deterministic data extrapolation from a clean periodic function with periodic components representation by a system of linear equations

Object forecasting has been a tedious task to be solved, such as money currency, stocks, and solar cycle predictions which are proved to be epitomes from objects that can be forecasted from periodic functions’ characteristic. The comparison between an unoptimized approach and an optimized approach to extrapolate a clean periodic function formed from a sum of periodic functions with integral periods has been proposed. Initially, both approaches will be utilized system of linear equations to identify periodic components which will be extracted using arithmetic means from matrix multiplication. The resulting optimized approach will have fewer runtimes, less memory allocation, and larger scope of periods than the unoptimized one. Furthermore, the optimized approach with different implementation will also be discussed to show how the computational technique can impact the efficiency of the solution. Two testing models are involved in this paper: the correctness test by source-code submission to Sphere Online Judge, and the performance test by generating their chart of runtimes and standard deviation. These models have shown that the efficient implementation with optimized approach can be entitled as the first rank solution in Sphere Online Judge.