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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...
9 years 前
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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...
9 years 前
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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...
9 years 前
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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...
9 years 前
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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...
9 years 前
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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...
9 years 前
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Friedrich Bauer
Fritz Bauer, eminent German computer scientist and last surviving member of the organizing committee of the 1964 Gatlingburg...
9 years 前
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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...
9 years 前
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Parallel Random Number Generators
This is the second of a multi-part series about the MATLAB random number generators. If you ask for help rng, you will get...
9 years 前
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Random Number Generators, Mersenne Twister
This is the first of a multi-part series about the MATLAB random number generators....
9 years 前
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Experiencing the MATLAB Watch
My experience with the forthcoming MATLAB watch exceeds my most optimistic expectations. The watch has not yet been...
9 years 前
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An Ornamental Geometric Inequality
I came across this "ornamental geometric inequality" in a tribute to Lothar Collatz....
9 years 前
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Triple Precision Accumlated Inner Product
Single and double precision are combined to facilitate a triple precision accumulated inner product....
9 years 前
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Iterative Refinement for Solutions to Linear Systems
Iterative refinement is a technique introduced by Wilkinson for reducing the roundoff error produced during the solution of...
9 years 前
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Origins of Colormaps
Steve Eddins has recently posted a series in his blog about colormaps. I want to add one more post. With release R2014b, we...
9 years 前
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The Three n Plus One Conjecture
If $n$ is odd, replace $n$ by $3n+1$, if not, replace $n$ by $n/2$. Repeat. A famous conjecture made by Lothar Collatz is...
9 years 前
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Prime Spiral
The prime spiral was discovered by Stanislaw Ulam in 1963, and featured on the cover of Scientific American in March,...
9 years 前
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Season’s Greetings, 2014
Season's Greetings, 2014 help greetings % greetings Seasonal holiday fractal. % greetings(phi) generates a...
9 years 前
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Jahnke and Emde, Revisited
An incredible book, published in several editions from 1909 to 1933, by German mathematicians Eugene Jahnke and Fritz Emde,...
9 years 前
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MathWorks Logo, Part Five, Evolution of the Logo
Our plots of the first eigenfunction of the L-shaped membrane have changed several times over the last fifty years.... read...
9 years 前
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MathWorks Logo, Part Four, Method of Particular Solutions Generates the Logo
The Method of Particular Solutions computes a highly accurate approximation to the eigenvalue we have been seeking, and...
9 years 前
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MathWorks Logo, Part Three, PDE Toolbox
The Partial Differential Equation Toolbox contains tools for the analysis of PDEs in two space dimensions and time. It is...
9 years 前
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MathWorks Logo, Part Two. Finite Differences
After reviewing the state of affairs fifty years ago, I use classic finite difference methods, followed by extrapolation, to...
10 years 前
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MathWorks Logo, Part One. Why Is It L Shaped?
MathWorks is the only company in the world whose logo satisfies a partial differential equation. Why is the region for this...
10 years 前
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Finite Fourier Transform Matrix
This is the third in a series of posts on the finite Fourier transform. The Fourier matrix produces an interesting graphic...
10 years 前
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FFT, Fast Finite Fourier Transform
This is the second in a series of three posts about the Finite Fourier Transform. This post is about the fast FFT algorithm...
10 years 前
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Touch-Tone Telephone Dialing
We all use Fourier analysis every day without even knowing it. Cell phones, disc drives, DVDs, and JPEGs all involve fast...
10 years 前
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Complete Pivoting and Hadamard Matrices
For several years we thought Hadamard matrices showed maximum element growth for Gaussian elimination with complete...
10 years 前
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Gaussian Elimination with Partial Pivoting
In rare cases, Gaussian elimination with partial pivoting is unstable. But the situations are so unlikely that we continue...
10 years 前
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Floating Point Denormals, Insignificant But Controversial
Denormal floating point numbers and gradual underflow are an underappreciated feature of the IEEE floating point standard....
10 years 前
