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The Eigenwalker Model of the Human Gait
A model of the human gait, developed by Nikolaus Troje, is a five-term Fourier series with vector-valued coefficients that...

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Dark Energy Gravitational Waves
Recent theoretical, observational and computational results establish the possibility that gravitational waves produced by...

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Numerical Computing with MATLAB
Toolbox containing files and app from Numerical Computing with MATLAB

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Piet Hein, Super Ellipses and Soma Cubes
An extraordinarily creative Danish mathematician, inventor, and poet who often wrote under the Old Norse pseudonym...

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Investigating the Classic Crossed Ladders Puzzle
Today's blog post is a complete working MATLAB program investigating the crossed ladders problem. Download a copy of the...

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The Classic Crossed Ladders Puzzle
Here is a classic puzzle. A pair of ladders leaning against the sides of an alley form a lopsided cross. Each ladder is...

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Experiments with MATLAB
Apps from Experiments with MATLAB

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How Many Times Should You Shuffle the Cards?
We say that a deck of playing cards is completely shuffled if it is impossible to predict which card is coming next when...

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Perfect Shuffles of Playing Cards
When a deck of playing cards is shuffled perfectly, the result is not random. A perfect shuffle places the cards in a...

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Fractal Global Behavior of Newton’s Method
When the starting point of Newton's method is not close to a zero of the function, the global behavior can appear to be...

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Testing Zero Finders
Use the historic cubic polynomial $x^3 - 2x - 5$ to test a few zero-finding algorithms. ...

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A Historic Cubic
The cubic polynomial $x^3 - 2x - 5$ has a unique place in the history of numerical methods....

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John Todd, Savior of Oberwolfach
This is the story of how John Todd saved what was to become one of the world's most important research institutions from...

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Trip Report: SuperComputing 2015
SC15, the International Conference for High Performance Computing, Networking, Storage and Analysis, was held in Austin,...

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Zeroin, Part 3: MATLAB Zero Finder, FZERO
MATLAB adds capability to search for an interval with a sign change....

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Zeroin, Part 2: Brent’s Version
Richard Brent's improvements to Dekker's zeroin algorithm, published in 1971, made it faster, safer in floating point...

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Zeroin, Part 1: Dekker’s Algorithm
Th. J. Dekker's zeroin algorithm from 1969 is one of my favorite algorithms. An elegant technique combining bisection and...

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Charles Lawson, 1931 – 2015
Chuck Lawson passed away in July at the age of 83. Chuck was one of the people who introduced me to computing and...

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Trip Report: Trefethen Birthday Conference
"New Directions in Numerical Computation" was a conference in celebration of Nick Trefethen's 60th birthday held August...

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Golub Matrices, Deceptively Ill Conditioned
I got the idea for these test matrices from Gene Golub years ago, but the mathematical foundation comes from a paper by...

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Tumbling Box ODE
A rectangular box, such as a book or a cell phone, thrown in the air can tumble stably about its longest axis, or about its...

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Discover e with a graphical experiment
An interactive graphical experiment lets you discover the value of one of the most important numerical quantities in...

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Trip Report: NACONF 2015 and Sparse Days III
I have just returned from two meetings in Europe, the 26th Biennial Conference on Numerical Analysis at the University of...

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Dubrulle Creates A Faster Tridiagonal QR Algorithm
Augustin (Austin) Dubrulle deserves to be better known in the numerical linear algebra community. His version of the...

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ALGOL 60, PL/0 and MATLAB
The 1960 programming language ALGOL 60 influenced the design of many subsequent languages, including C and a miniature...

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Friedrich Bauer
Fritz Bauer, eminent German computer scientist and last surviving member of the organizing committee of the 1964 Gatlingburg...

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Accuracy of eig in support of complex step differentation: Derivative estimate accuracy degrades when step gets too small
I had forgotten about Nick Higham's comment after my blog post referencing his paper, "The complex step approximation to the Fr...

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Accuracy of eig in support of complex step differentation: Derivative estimate accuracy degrades when step gets too small
But you should not have to resort to complex step differentiation because an analytic expression for the derivative of an eigenv...

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Accuracy of eig in support of complex step differentation: Derivative estimate accuracy degrades when step gets too small
I have to admit that I am unsure about what is going on here. Complex step differentiation relies upon the unperturbed function...

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The Ziggurat Random Normal Generator
This is the third in a multi-part series on the MATLAB random number generators. MATLAB has used variants of George...

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