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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...

casi 11 años hace | 2

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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...

casi 11 años hace

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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...

casi 11 años hace

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Random Number Generators, Mersenne Twister
This is the first of a multi-part series about the MATLAB random number generators....

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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...

casi 11 años hace

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An Ornamental Geometric Inequality
I came across this "ornamental geometric inequality" in a tribute to Lothar Collatz....

alrededor de 11 años hace

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Triple Precision Accumlated Inner Product
Single and double precision are combined to facilitate a triple precision accumulated inner product....

alrededor de 11 años hace

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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...

alrededor de 11 años hace

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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...

alrededor de 11 años hace

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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...

alrededor de 11 años hace

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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,...

alrededor de 11 años hace

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Season’s Greetings, 2014
Season's Greetings, 2014 help greetings % greetings Seasonal holiday fractal. % greetings(phi) generates a...

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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,...

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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...

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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...

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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...

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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...

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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...

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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...

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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...

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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...

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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...

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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...

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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....

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Floating Point Numbers
This is the first part of a two-part series about the single- and double precision floating point numbers that MATLAB uses...

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Householder Symposium XIX Trip Report
The nineteenth Householder Symposium, Householder XIX, was held June 8-13 at Sol Cress, a conference center near Spa,...

casi 12 años hace

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Ordinary Differential Equations, Stiffness
Stiffness is a subtle concept that plays an important role in assessing the effectiveness of numerical methods for ordinary...

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Ordinary Differential Equation Solvers ODE23 and ODE45
The functions ode23 and ode45 are the principal MATLAB and Simulink tools for solving nonstiff ordinary differential...

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Ordinary Differential Equation Suite
MATLAB and Simulink have a powerful suite of routines for the numerical solution of ordinary differential equations. ...

casi 12 años hace

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Periodic Solutions to the Lorenz Equations
Changing the value of a parameter in the equations that produce the famous Lorenz chaotic attractor yields nonlinear...

casi 12 años hace