Harvard AM205 video 0.2 - Sources of error

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Harvard Applied Math 205 is a graduate-level course on scientific computing and numerical methods. This video provides an introduction to the field of scientific computing. It provides historical context and presents some modern examples.

  1. Chris Rycroft
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Hello @chrisrycroft2010,
I really like the lecture series..
Could you please explain how the second term in the inequality gets eps*f(x)/h term? Why is not eps or any other expression? Thanks!

buae
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🎯 Key Takeaways for quick navigation:

📊 Error analysis is fundamental in scientific computing, involving both modeling and numerical sources of error.
🔄 Truncation or discretization error arises from approximating continuous processes with discrete calculations, such as finite differences or series truncation.
💻 Rounding error occurs due to finite precision arithmetic in computers, where small errors accumulate during arithmetic operations.
📉 Discretization error often dominates in practice over rounding error, impacting the accuracy of numerical computations.
📈 Error behavior changes with the choice of discretization parameter \( h \), with a minimum point indicating the transition from dominant discretization to dominant rounding error.
📉 Error plots, especially on logarithmic scales, help analyze error behavior and confirm convergence of numerical methods.
🔍 Relative error, though more informative in some cases, poses challenges when the true value is unknown or close to zero.
📐 Log-log plots are useful for deducing algebraic convergence, while semi-log plots are suitable for detecting exponential convergence in error decay.

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