Numerical Computing Formalism

Abstract

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