Brute Force Discretization  Python for Integrated Circuits   An Online Book  

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


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================================================================================= Brute force discretization is a straightforward and computationally intensive method used in various fields of science and engineering to approximate continuous functions or processes by dividing them into discrete parts. This approach involves subdividing a continuous domain or range into a finite number of discrete intervals or values and then calculating or approximating the function's behavior within each interval. It's called "brute force" because it doesn't rely on sophisticated algorithms or optimizations; instead, it simply involves a systematic enumeration of all possible values within the discretized space. Here are a few examples of where brute force discretization is commonly used:
While brute force discretization can be conceptually simple, it often leads to a tradeoff between accuracy and computational cost. As you increase the granularity of the discretization (i.e., using smaller intervals or more discrete points), you get a more accurate approximation, but it requires more computational resources. Conversely, coarser discretization may be computationally efficient but less accurate. In practice, people often seek more efficient methods, such as adaptive discretization or specialized algorithms, to strike a balance between accuracy and computational cost, especially when dealing with complex and highdimensional problems. ============================================


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