Interpolation and the cotanc function
This weekend I wrote three posts related to interpolation: Compression and interpolation Bessel, Everett, and Lagrange interpolation Binomial coefficients with non-integer arguments The first post looks at reducing the size of mathematical tables by switching for linear to quadratic interpolation. The immediate application is obsolete, but the principles apply to
Read moreExploring 21 Unique Custom Cursors for Your Site
Microinteractions play an role in creating engaging and intuitive user experiences. These subtle animations and feedback can guide users, provide valuable information, and make interactions more enjoyable and generally look cool! One often overlooked yet super powerful micro-interaction is the use of custom cursors. Custom cursors can add a unique touch
Read moreBinomial coefficients with non-integer arguments
When n and r are positive integers integers, with n ≥ r, there is an intuitive interpretation of the binomial coefficient C(n, r), namely the number of ways to select r things from a set of n things. For this reason C(n, r) is usually pronounced “n choose r.” But
Read moreBessel, Everett, and Lagrange interpolation
I never heard of Bessel or Everett interpolation until long after college. I saw Lagrange interpolation several times. Why Lagrange and not Bessel or Everett? First of all, Bessel interpolation and Everett interpolation are not different kinds of interpolation; they are different algorithms for carrying out the same interpolation as
Read moreCompression and interpolation
Data compression is everywhere. We’re unaware of it when it is done well. We only become aware of it when it is pushed too far, such as when a photo looks grainy or fuzzy because it was compressed too much. The basic idea of data compression is to not transmit
Read moreBattling ticket bots and untangling taxes at the frontiers of e-commerce
On today's episode we chat with Ilya Grigorik, a Distinguished Engineer and Technical Advisor to the CEO at Shopify. From battling hordes of bots trying to scalp seats before humans can get their hands on concert tickets, to automatically handling relevant tax codes and regulations across countries and states so
Read moreChebyshev polynomials as distorted cosines
Forman Acton’s book Numerical Methods that Work describes Chebyschev polynomials as cosine curves with a somewhat disturbed horizontal scale, but the vertical scale has not been touched. The relation between Chebyshev polynomials and cosines is Tn(cos θ) = cos(nθ). Some sources take this as the definition of Chebyshev polynomials. Other
Read moreMomento Migrates Object Cache as a Service to Ampere Altra
Explore Momento's serverless cache on Ampere-powered Google Tau T2A, simplifying cloud app performance with automated resource management and high scalability. Continue reading Momento Migrates Object Cache as a Service to Ampere Altra on SitePoint.
Read morePractical tips for retrieval-augmented generation (RAG)
Retrieval-augmented generation (RAG) is one of the best (and easiest) ways to specialize an LLM over your own data, but successfully applying RAG in practice involves more than just stitching together pretrained models.
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