Notes concerning “Math”

• The Gelfand Principle, or how to choose educational examples 2007 to 2009 (8 minutes)
• Additive smoothing for Markov models 2007 to 2009 (updated 2019-05-19) (11 minutes)
• In what sense is e the optimal branching factor, and what does it mean for menu tree design? 2012-12-04 (3 minutes)
• Worst-case-logarithmic-time reduction over arbitrary intervals over arbitrary semigroups 2012-12-04 (5 minutes)
• a logarithmic-time alternative to summed-area tables for reducing arbitrary semigroup operations over arbitrary ranges (a generalization of RMQ segment trees) 2012-12-06 (updated 2013-05-17) (10 minutes)
• Achieving smooth curves in scanline image generation 2013-05-17 (1 minute)
• Constructing error-correcting codes using Hadamard transforms 2013-05-17 (updated 2013-05-20) (22 minutes)
• Square wave synthesis 2014-02-24 (2 minutes)
• Bottle washing 2014-04-24 (7 minutes)
• Fixed point 2014-04-24 (1 minute)
• lattices, powersets, bitstrings, and efficient OLAP 2014-04-24 (17 minutes)
• Polynomial-spline FIR kernels by integrating sparse kernels 2014-04-24 (12 minutes)
• Very composite numbers 2014-04-24 (4 minutes)
• Ideas to ship in 2014 2014-04-24 (updated 2019-05-05) (35 minutes)
• An algebraic approach to 3D geometry 2014-06-03 (updated 2014-06-29) (22 minutes)
• Division 2014-06-05 (14 minutes)
• Rendering iterated function systems (IFSes) with interval arithmetic 2014-09-02 (6 minutes)
• Ternary mergesort 2015-09-03 (2 minutes)
• Very fast FIR filtering with time-domain zero stuffing and splines 2015-09-03 (updated 2015-09-07) (13 minutes)
• Convolution surface plotting 2015-09-03 (updated 2015-09-13) (2 minutes)
• Convolution with intervals 2015-09-07 (1 minute)
• Circle-portal GUI 2016-06-03 (11 minutes)
• Gaussian spline reconstruction 2016-06-05 (updated 2016-06-06) (5 minutes)
• Further notes on algebras for dark silicon 2016-09-17 (updated 2017-04-18) (23 minutes)
• Changing the basis to a more expressive one with better affordances 2016-09-29 (5 minutes)
• Counting the number of spaces to the left in parallel 2016-10-11 (5 minutes)
• Analogies between spring–mass–dashpot systems, electrical systems, and fluidic systems 2016-10-30 (4 minutes)
• Academic lineage 2016-10-30 (updated 2019-11-24) (15 minutes)
• Using Aryabhata’s pulverizer algorithm to calculate multiplicative inverses in prime Galois fields and other multiplicative groups 2017-01-06 (updated 2019-07-05) (4 minutes)
• What is the type of lerp? 2017-01-08 (5 minutes)
• Reduced affine arithmetic raytracer 2017-05-10 (1 minute)
• Golomb-coding operands as belt offsets likely won’t increase code density much 2017-06-15 (updated 2017-06-20) (6 minutes)
• Cheap frequency detection 2017-06-29 (updated 2019-06-19) (50 minutes)
• Vectorized prefix sum 2017-07-19 (5 minutes)
• Xor 1 to 1 hashing 2017-07-19 (updated 2017-08-03) (10 minutes)
• Affine arithmetic optimization 2017-07-19 (updated 2019-09-15) (3 minutes)
• The tangent of the sum of two angles 2018-04-27 (1 minute)
• Caustic simulation 2018-09-10 (updated 2018-11-04) (2 minutes)
• Quintic upsampling of time-series with 1½ multiplies per sample 2018-10-28 (2 minutes)
• Time domain analog chaos 2018-10-28 (4 minutes)
• Sparse filters 2018-12-02 (4 minutes)
• Real-time bokeh algorithms, and other convolution tricks 2018-12-18 (updated 2019-08-15) (23 minutes)
• Accelerating Euler’s Method on linear time-invariant systems by exponentiating matrices 2019-03-24 (updated 2019-04-02) (7 minutes)
• Solving initial-value problems faster and with guaranteed error bounds with affine arithmetic 2019-04-02 (5 minutes)
• Karatsuba 2019-04-20 (2 minutes)
• When should you give up waiting for the bus and just walk? 2019-04-24 (5 minutes)
• Dercuano formula display 2019-04-30 (5 minutes)
• Why the Cartesian product of fields isn’t a field 2019-05-02 (2 minutes)
• An algebra of textures for interactive composition 2019-05-08 (4 minutes)
• On the method of finite differences used in Babbage’s Difference Engine 2019-05-31 (6 minutes)
• Midpoint method texture mapping 2019-06-01 (3 minutes)
• Smooth hysteresis 2019-06-11 (13 minutes)
• Reducing the cost of self-verifying arithmetic with array operations 2019-06-23 (15 minutes)
• Fermat primes 2019-07-07 (4 minutes)
• A failed attempt to make squares cheaper to compute 2019-07-09 (updated 2019-07-11) (4 minutes)
• Using the method of secants for general optimization 2019-07-22 (updated 2019-11-26) (13 minutes)
• Human memorable secret sharing 2019-08-10 (2 minutes)
• The miraculous low-rank SVD approximate convolution algorithm 2019-08-14 (updated 2019-08-15) (31 minutes)
• Complex linear regression (in the field ℂ of complex numbers) 2019-08-17 (updated 2019-08-18) (9 minutes)
• Robust local search in vector spaces using adaptive step sizes, and thoughts on extending quasi-Newton methods 2019-08-17 (updated 2019-09-15) (15 minutes)
• Some notes on the landscape of linear optimization software and applications 2019-08-21 (updated 2019-08-25) (35 minutes)
• Differentiable neighborhood regression 2019-08-31 (15 minutes)
• Everything is money? 2019-08-31 (4 minutes)
• Image filtering with an approximate Gabor wavelet or Morlet wavelet using a cascade of sparse convolution kernels 2019-08-31 (updated 2019-09-08) (28 minutes)
• Cloth structure from shading 2019-09-01 (2 minutes)
• Processing halftoning 2019-09-01 (15 minutes)
• A bag of candidate techniques for sparse filter design 2019-09-01 (18 minutes)
• Dercuano plotting 2019-09-03 (updated 2019-09-05) (34 minutes)
• A formal language for defining implicitly parameterized functions 2019-09-05 (updated 2019-09-30) (29 minutes)
• Pythagorean cement pipes for your shower singing 2019-09-08 (updated 2019-09-09) (7 minutes)
• Fast mathematical optimization with affine arithmetic 2019-09-15 (5 minutes)
• An affine-arithmetic database index for rapid historical securities formula queries 2019-09-15 (15 minutes)
• Sparse sinc 2019-09-15 (10 minutes)
• Hadamard rhythms 2019-11-01 (6 minutes)
• Sparse filter optimization 2019-11-01 (5 minutes)
• Interval raymarching 2019-11-02 (updated 2019-11-10) (6 minutes)
• Some thoughts on SDF raymarching 2019-11-11 (updated 2019-12-10) (31 minutes)
• Rediscovering successive parabolic interpolation: derivative-free optimization of scalar functions by fitting a parabola 2019-11-26 (updated 2019-11-27) (8 minutes)