Posts 21 - 30 of 40

Results for: Eigenvalues

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 mathematically precise order. As a result, when the most common version of a perfect shuffle is repeated eight times, the deck returns to its original state.... read more >>

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 the secant method for finding a zero of a function of a real variable, it has become fzero in MATLAB today. This is the first of a three part series.... read more >>

Tumbling Box ODE 2

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 shortest axis, but not about its middle axis.... read more >>

Friedrich Bauer 5

Fritz Bauer, eminent German computer scientist and last surviving member of the organizing committee of the 1964 Gatlingburg Conference on Numerical Algebra, passed away on March 26 at the age of 90.... read more >>

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 guaranteed bounds on the accuracy. It also provides flexibility involving the boundary conditions that leads to the MathWorks logo. ... read more >>

MathWorks Logo, Part Three, PDE Toolbox 2

The Partial Differential Equation Toolbox contains tools for the analysis of PDEs in two space dimensions and time. It is perhaps not surprising that one of the primary examples involves the L-shaped membrane.... read more >>

MathWorks Logo, Part Two. Finite Differences 2

After reviewing the state of affairs fifty years ago, I use classic finite difference methods, followed by extrapolation, to find the first eigenvalue of the region underlying the MathWorks logo.... read more >>

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 equation shaped like a capital letter L? ... read more >>

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 and has a surprising eigenvalue distribution. ... read more >>

Singular Value Analysis of Cryptograms

The Singular Value Decomposition of the digram frequency matrix of a text coded with a simple substitution cypher can reveal information about the vowels and consonants in the text. ... read more >>

Posts 21 - 30 of 40