Numerical application of mean value theorem
Suppose you’d like to evaluate the function for small values of z, say z = 10−8. This example comes from [1]. The Python code from numpy import exp def f(z): return (exp(z) - 1 - z)/z**2 print(f(1e-8)) prints -0.607747099184471. Now suppose you suspect numerical difficulties and compute your result to
Read moreNumerical differentiation with a complex step
The most obvious way to approximate the derivative of a function numerically is to use the definition of derivative and stick in a small value of the step size h. f′ (x) ≈ ( f(x + h) − f(x) ) / h. How small should h be? Since the exact value
Read moreReshaping the future of API platforms
Marco Palladino, CTO and cofounder of cloud-native API gateway Kong, talks with Ryan about the complexities of multi-cloud Kubernetes architecture, how AI has the potential to improve infrastructure management, and how Kong’s large action model will reshape the future of API platforms.
Read moreMCMC and the coupon collector problem
Bob Carpenter wrote today about how Markov chains cannot thoroughly cover high-dimensional spaces, and that they do not need to. That’s kinda the point of Monte Carlo integration. If you want systematic coverage, you can/must sample systematically, and that’s impractical in high dimensions. Bob gives the example that if you
Read moreChris Corner: Unusual Ideas with Great Results
SVG Short Circuiting SVG is normally a pretty efficient file format. If an image is vector in nature, leaving it as vector is normally a good plan as it will like scale well and look pretty darn crips. But of course, It Depends. Super complex vector graphics can get huge,
Read moreUp and down the abstraction ladder
Gian-Carlo Rota made a profound observation on the application of theory. One frequently notices, however, a wide gap between the bare statement of a principle and the skill required in recognizing that it applies to a particular problem. This isn’t quite what he said. I made two small edits to
Read moreThe reverse mullett model of software engineering
Ben and Ryan are joined by software developer and listener Patrick Carlile for a conversation about how the job market for software engineers has changed since the dot-com days, navigating boom-and-bust hiring cycles, and the developers finding work at Walmart and In-N-Out. Plus: “Party in the front, business in the
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