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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...

11년 초과 전 | 2

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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...

11년 초과 전 | 2

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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...

11년 초과 전 | 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...

11년 초과 전

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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...

11년 초과 전

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

11년 초과 전

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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...

11년 초과 전

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

11년 초과 전

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

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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...

11년 초과 전

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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...

11년 초과 전

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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...

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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,...

거의 12년 전

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

거의 12년 전

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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,...

거의 12년 전

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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...

거의 12년 전

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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...

거의 12년 전

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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...

대략 12년 전

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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...

대략 12년 전

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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....

대략 12년 전

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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,...

12년 초과 전

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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...

12년 초과 전