Numerical Computing Formalism

Abstract

Numerical computation enables you to compute solutions to numerical problems, provided you can frame them into a proper format. This requires certain considerations. For example, if you digitize continuous functions, then you are going to introduce certain errors due to the sampling at a finite frequency. Hence, a very accurate result would require very a fast sampling rate. When a large data set needs to be computed, it becomes a computationally intensive and time consuming task. Also you must understand that the numerical solutions are an approximation at best, compared to analytical solutions. The onus of finding their physical meaning and significance lies on you. The art of discarding solutions that do not have meaning in real world scenarios is something that a scientist/engineer develops over the years. Also, a computational device is only as intelligent as its operator. The law of GIGO (garbage-in-garbage-out) is followed very strictly in this domain.