My favorite paper: H = W
A paper came out in 1964 with the title “H = W.” The remarkably short title was not cryptic, however. The people for whom the paper was written knew exactly what it meant. There were two families of function spaces, one denoted with H and another denoted with W, that were
Read moreCan a dev environment spark joy? The Android team thinks so.
Matthew McCullough, VP of Product for Android Developer Experience, sits down with Ryan to talk advancements in Android development, enhancing developer efficiency and reducing routine toil, and the application of Gemini AI models to improve software toolchains.
Read moreWilkinson’s polynomial
If you change the coefficients of a polynomial a little bit, do you change the location of its zeros a little bit? In other words, do the roots of a polynomial depend continuously on its coefficients? You would think so, and you’d be right. Sorta. It’s easy to see that
Read moreHow to Build Scalable Web Apps with React JS
Unlock the best practices for building scalable React apps. Explore strategies for performance, maintainability, state management, code splitting, and real-world success stories. Continue reading How to Build Scalable Web Apps with React JS on SitePoint.
Read moreInterpolation instability
You would think that interpolating at more points would give you a more accurate approximation. There’s a famous example by Runge that proves this is not the case. If you interpolate the function 1/(1 + x²) over the interval [−5, 5], as you add more interpolation points the maximum interpolation
Read moreThe Ampere Porting Advisor Tutorial
This tutorial walks you through building and using the Ampere Porting Advisor and how to mitigate any issues. Continue reading The Ampere Porting Advisor Tutorial on SitePoint.
Read moreDrazin pseudoinverse
The most well-known generalization of the inverse of a matrix is the Moore-Penrose pseudoinverse. But there is another notion of generalized inverse, the Drazin pseudoinverse, for square matrices. If a matrix A has an inverse A−1 then it also has a Moore-Penrose pseudoinverse A+ and a Drazin pseudoinverse AD and A−1 =
Read moreEffective graph resistance
I’ve mentioned the Moore-Penrose pseudoinverse of a matrix a few times, most recently last week. This post will give an application of the pseudoinverse: computing effective graph resistance. Given a graph G, imagine replacing each edge with a one Ohm resistor. The effective resistance between two nodes in G is the electrical
Read moreMultiplying a matrix by its transpose
An earlier post claimed that there practical advantages to partitioning a matrix, thinking of the matrix as a matrix of matrices. This post will give an example. Let M be a square matrix and suppose we need to multiply M by its transpose MT. We can compute this product faster than
Read moreA bit-twiddling marvel
Pop quiz: what does the following code do? bool is_leap_year_fast(uint32_t y) { return ((y * 1073750999) & 3221352463) <= 126976; } It determines whether the year y is a leap year in the Gregorian calendar, of course. :) It’s very efficient, though I don’t image that would ever matter. But
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