Analytical differentiation of a function is always feasible, regardless of its complexity, provided the function is explicitly defined. Computer algebra systems, such as Mathematica [7] and Wolfram Alpha, can differentiate any analytical function exactly. Numerical differentiation becomes necessary only when a function is provided in a numerical form. Consider Table 5.1 which defines \( f(x) \) numerically.

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Numerical Differentiation

  • Seiichi Nomura

摘要

Analytical differentiation of a function is always feasible, regardless of its complexity, provided the function is explicitly defined. Computer algebra systems, such as Mathematica [7] and Wolfram Alpha, can differentiate any analytical function exactly. Numerical differentiation becomes necessary only when a function is provided in a numerical form. Consider Table 5.1 which defines \( f(x) \) numerically.