Discretization Error  Python for Integrated Circuits   An Online Book  

Python for Integrated Circuits http://www.globalsino.com/ICs/  


Chapter/Index: Introduction  A  B  C  D  E  F  G  H  I  J  K  L  M  N  O  P  Q  R  S  T  U  V  W  X  Y  Z  Appendix  
================================================================================= Discretization error, often referred to as discretization error or numerical error, is a type of error that occurs when continuous data or processes are approximated or represented using discrete values or methods. It is a common issue in various fields, including mathematics, computer science, and engineering, where continuous problems need to be solved using finite and discrete techniques. Discretization error can manifest in several ways:
Managing discretization errors often involves a tradeoff between computational efficiency and accuracy. Smaller discretization steps and more refined methods generally reduce error but increase computational costs. Engineers and scientists must carefully choose appropriate discretization techniques and parameters to balance these considerations and obtain accurate results in numerical simulations and analyses. Additionally, error analysis and convergence studies are often performed to assess and quantify the discretization errors in numerical computations. Generalization error (see Probability Bounds Analysis (PBA) at page3947) sometimes can be given by.  [3929a] The first term in the bracket is from the finite hypothesis case, while the second term is discretization error, (see page3929) coming from the KLipschitzness. Since the first term depends on log(1/ϵ) and increases very slowly as ϵ goes to 0, and the second term depends on ϵ, there is trading off between the two. Therefore, sometime, you can ignore the second term when ϵ is close to 0. ============================================


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